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5/18/26, 8:20 AMPlenary Talk
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Julianne Chung (Emory University)5/18/26, 8:30 AM
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include computations of inner-products, which becomes costly when the number of iterations is high, are a bottleneck for parallelization, and can cause the algorithms to break down due to information loss in the projections.
In this talk, I...
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Hugo Woerdeman (Drexel University)5/18/26, 9:25 AM
After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the settings of sequence spaces $\ell^p$ (including the finite dimensional case), the associated function space $\ell_A^p$, Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in ${\mathbb C}^n$, as well as the Hardy space on the polydisk and half-space....
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ILIAS KOTSIREAS (WILFRID LAURIER UNIVERSITY)5/18/26, 11:00 AMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
It is widely acknowledged that the search for Legendre pairs of higher orders presents a significant challenge. Therefore, rather than engaging in traditional, computationally intensive combinatorial searches, one might consider exploring Legendre pairs via structured matrices.
In this talk, we explore Legendre pairs through matrix structures and use compressed sequences to search for...
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Nathan Lindzey (University of Memphis)5/18/26, 11:00 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
A family of permutations $\mathcal{F} \subseteq S_n$ is even-cycle-intersecting if $\sigma \pi^{-1}$ has an even cycle for all $\sigma,\pi \in \mathcal{F}$. We show that if $\mathcal{F} \subseteq S_n$ is an even-cycle-intersecting family of permutations, then $|\mathcal{F}| \leq 2^{n-1}$, and that equality holds when $n$ is a power of 2 and $\mathcal{F}$ is a double-translate of a Sylow...
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Dr Ethan Epperly (UC Berkeley)5/18/26, 11:00 AM
The fundamental building blocks of iterative linear algebra algorithms in ordinary digital computation are matrix–vector multiplications and inner products. In quantum computing, we lose easy access to both primitives. But we also gain replacements. Instead of matrix–vector products, we can apply the unitary time evolution operator $e^{-itA}$, and we have access to noisy—but statistically...
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Delio Jaramillo Velez (Virginia Tech)5/18/26, 11:00 AM
A connected dominating set of a graph is a vertex set that induces a connected subgraph and such that every vertex outside the set is adjacent to at least one vertex in the set. The minimum cardinality of a connected dominating set is called the connected domination number. We present an algebraic expression for this combinatorial invariant using the theory of binomial edge ideals.
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Giriraj Ghosh (Indian Institute of Technology Kharagpur, India)5/18/26, 11:00 AM
We study the structure of persistent modules over arbitrary coefficient fields and related algebraic systems, with an emphasis on explicit basis constructions and algorithmic realizations rooted in linear algebra. Persistent homology assigns to a filtered topological space a persistence module, traditionally decomposed via the structure theorem over a field. However, extending such...
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Stephen Thomas (Lehigh University)5/18/26, 11:00 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
Krylov subspace methods are widely used finite-memory algorithms, yet several well-known practical behaviors remain only partially understood within classical orthogonality-based analysis. These include the frequent failure of restarted methods, the success of truncated and s-step recurrences, and the large difference between truncation depth and restart length observed in applications.
In...
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Arjun Vijaywargiya (University of Texas at Austin)5/18/26, 11:00 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori–Zwanzig (MZ) perspective, projecting the full dynamics onto a low-dimensional resolved subspace induces additional noise and memory terms arising from the dynamics of the unresolved component in the orthogonal...
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Vanni Noferini (Aalto University)5/18/26, 11:00 AM
Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework described in [M. Gnazzo, V. Noferini, L. Nyman, F. Poloni, Riemann-Oracle: A general-purpose Riemannian optimizer to solve nearness problems in matrix...
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Prof. Shmuel Friedland (University of Illinois Chicago)5/18/26, 11:00 AM
In this talk we survey some recent results on entanglement and separability of general, symmetric (bosons), skew-symmetric (fermions) tensors, and their computability. All these results are related to corresponding numerical radii. This talk is based on the arXiv preprint
S. Friedland, Tensors, entanglement, separability, and their complexity, arXiv:2509.21639, 2025.
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Alex Gorodetsky (University of Michigan)5/18/26, 11:00 AMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a difficult problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are...
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Steven Miller (Williams College)5/18/26, 11:00 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Random matrix theory has successfully modeled a variety of systems, from energy levels of heavy nuclei to zeros of the Riemann zeta function. One of the central results is Wigner's semi-circle law: the distribution of normalized eigenvalues for ensembles of real symmetric matrices converge to the semi-circle density (in some sense) as the matrix size tends to infinity. We introduce a new...
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Prof. Maria Isabel Bueno Cachadina (University of California Santa Barbara), Charles Kulick (University of California Santa Barbara)5/18/26, 11:00 AM
Generative AI has reshaped student behavior in linear algebra courses: attendance has declined, and traditional take-home assessments are increasingly vulnerable to “solution acquisition” rather than learning. We present a redesign for Applied Linear Algebra courses that treats generative AI not as a shortcut, but as a catalyst for disciplinary literacy.
We replace an exam-heavy structure...
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Igor Simunec (EPFL)5/18/26, 11:00 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard Arnoldi process. However, the resulting Hessenberg matrix is generally not similar to the one produced by the standard Arnoldi process, which can lead to delays or spike-like irregularities in convergence. In this...
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Dr Thijs Steel (KU Leuven)5/18/26, 11:00 AM
For small and/or dense generalized eigenvalue problems, the QZ method remains the method of choice because of its robustness. In this talk, we will discuss how that robustness may occasionally fail, especially if the matrices are badly scaled or singular. We will discuss how new deflation criteria and some changes in the preprocessing can improve the robustness.
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Adela DePavia (The University of Chicago)5/18/26, 11:00 AMNumerical Linear Algebra in Machine LearningMinisymposium Talk
Adaptive gradient optimization algorithms—including Adam, Adagrad, and their variants—have found widespread use in machine learning, signal processing, and many other settings. However many algorithms in this family are not rotationally equivariant: in this talk we examine how a simple change-of-basis in either parameter space or data space can drastically impact both the convergence rates and...
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Yunhui He (University of Houston)5/18/26, 11:25 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
In this talk, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and nonlinear problems. This allows flexibility to use different combinations of fixed-point iteration and Anderson iteration. We present a convergence analysis...
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Matteo Bertuzzo (Eindhoven University of Technology)5/18/26, 11:25 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
The injection metric measures the distance between two subspaces and naturally arises in the context of subspace coding, when the codewords potentially have different dimensions. In this talk, we consider a graph associated with the injection metric and examine how its structure determines the existence of good codes for subspace coding.
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Maria Trigueros (Benemérita Universidad Autónoma de Puebla, México)5/18/26, 11:25 AM
The use of real or realistic problems to introduce university students to linear algebra concepts through modeling has proven effective in stimulating student learning. We present an experience based on mathematical modeling and APOS theory (Action, Process, Object, and Schema) to introduce the concepts of matrix transformation and inverse matrix transformation in the context of an...
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Daniel Szyld (Temple University)5/18/26, 11:25 AMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
We extend results known for the randomized (point and block)
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Gauss-Seidel and the Gauss-Southwell methods for the case of a Hermitian and positive definite matrix to certain classes of non-Hermitian matrices. We consider cases with overlapping variables (as in Domain Decomposition). We obtain convergence results for a whole range of parameters describing the probabilities in the randomized... -
Nico Vervliet (KU Leuven)5/18/26, 11:25 AMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
We present new generic and deterministic uniqueness results for block term decompositions (BTD). These uniqueness conditions hold under mild assumptions and apply to more general settings than previously known results. We also present an algebraic algorithm for the computation of BTDs. Our algorithm requires no knowledge of the block sizes appearing in the BTD: these block sizes are recovered...
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Tomoki Koike (Georgia Institute of Technology)5/18/26, 11:25 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Modeling and simulation of real-world applications often involve dynamical systems with large degrees of freedom, requiring substantial computational time and resources. Projection-based model reduction enables efficient simulation of such dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. Specifically, Operator Inference (OpInf) learns such reduced...
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Kaustubh Roy (University of Manchester)5/18/26, 11:25 AMNumerical Linear Algebra in Machine LearningMinisymposium Talk
The CLASSIX algorithm is a fast and explainable approach to data clustering. In its original form, this method utilizes the first principal component of the data matrix to truncate the search for nearby data points, using the Cauchy-Schwarz inequality, with proximity being defined in terms of the Euclidean distance. In this work, we demonstrate methods to extend CLASSIX to other distance...
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Vilhelm P. Lithell (KTH Royal Institute of Technology)5/18/26, 11:25 AM
We are interested in an eigenvector-nonlinear eigenvalue problem (NEPv), that is, a problem of the form $A(x)x=\lambda x$, where $A:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n\times n}$ is symmetric, and the eigenvector has a prescribed norm, for instance $\Vert x \Vert = 1$. In this sense, this class of problems generalize the linear eigenvalue problem. Motivated by applications such as the...
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Dr Tejbir Tejbir (Indian Statistical Institute, Delhi Centre, India)5/18/26, 11:25 AM
Linear preserver problems study linear maps on matrix spaces that leave certain functions, subsets, or relations invariant, whereas matrix decomposition problems focus on expressing matrices as products of matrices with prescribed structural properties. An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals...
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Juan Zhang5/18/26, 11:25 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Our work presents a novel mixed precision formulation of the General Alternating-Direction Implicit (GADI) method, designed to accelerate the solution of large-scale sparse linear systems $Ax=b$. By solving the computationally intensive subsystems in low precision (e.g., Bfloat16 or FP32) and performing residual and solution updates in high precision, the proposed method significantly reduces...
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Motoyuki NOBORI (Graduate School of Science and Engineering, Ehime University)5/18/26, 11:25 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The main purpose of this presentation is to illustrate an equivalent condition for the equality case in the generalized Böttcher-Wenzel (BW) inequality for three matrices.
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Let $A, B,$ and $C$ be square matrices with complex elements. The BW inequality is an upper bound estimate on the Frobenius norm of the commutator of $A$ and $B$, defined as $AB-BA$. After the BW inequality was proved in... -
Zeguan Wu (University of Pittsburgh)5/18/26, 11:25 AM
Quantum computing relies heavily on the efficient manipulation of linear algebraic structures. This talk discusses the application of quantum linear algebra across two major domains: continuous optimization and differential equations. We demonstrate how quantum linear algebra can be utilized to solve these problems efficiently, discussing both the algorithmic construction and the theoretical...
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Volker Mehrmann (TU Berlin)5/18/26, 11:25 AM
We analyze the robust asymptotic stability under structure-preserving perturbations for the class of linear time-invariant dissipative-Hamiltonian differential-algebraic (dHDAE) systems. We show how to compute the distance to the nearest singular and high index system and determine stability radii for the finite spectrum under structure preserving perturbations
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Juan Pablo Serrano Perez (Cinvestav)5/18/26, 11:25 AM
The distance ideals of connected graphs are algebraic invariants extending the Smith normal form (SNF) and the spectrum of graph distance matrices.
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In general, distance ideals are not monotone under taking induced subgraphs.
However, it was proved in 2017 that the set of graphs with one trivial distance ideal over $\mathbb{Z}[X]$ and over $\mathbb{Q}[X]$ was characterized in terms... -
Gustaf Lorentzon (KTH)5/18/26, 11:25 AM
We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, using as few matrix-matrix multiplications as possible. Our approach to this problem involves studying the set $\Pi^*_{2^m}$, defined as the set of polynomials computable with at most $m$ matrix-matrix multiplications, but with an arbitrary number of matrix additions and scaling operations. This...
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Mr Bowen Gao (Fudan University)5/18/26, 11:50 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Mixed precision computation has attracted great attention in recent years partly due to the evolution of machine learning and hardware infrastructure. Recent development on mixed precision algorithms has largely enhanced the performance of various linear algebra solvers. In this talk, we propose a mixed precision algorithm for the computation of matrix root functions, primarily the matrix...
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Simon Mataigne (UCLouvain)5/18/26, 11:50 AM
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by Hüper et al. (2021), which contains the well-known Euclidean and canonical metrics. First, we give the best Lipschitz constants between the distances induced by any two members of the...
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Michael Tait (Villanova University)5/18/26, 11:50 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
We discuss the use of graph theory methods to attack coding theory problems.
This is joint work with Aida Abiad and Harper Reijnders.
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Francoise Tisseur (The University of Manchester)5/18/26, 11:50 AM
Optimal damping aims at determining a vector of damping coefficients $\nu$ that maximizes the decay rate of a mechanical system's response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov equation whose coefficient matrix depends on $\nu$. For physical relevance, the damping coefficients must be nonnegative and the resulting system must be...
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Tom Werner (TU Braunschweig)5/18/26, 11:50 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
In this talk, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov ) to solve systems of nonlinear equations. Building on the recent development of nlTGCR as well as earlier work on classical GCR-like linear Krylov solvers such as GMRESR, we generalize these approaches to non-linear problems via nested algorithmic structures. We establish connections of nlKrylov...
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Fuzhen Zhang (Nova Southeastern University)5/18/26, 11:50 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Normal matrices form a central class in matrix analysis, including Hermitian, skew-Hermitian, and unitary, positive semidefinite, permutation matrices and so on. This presentation surveys fundamental properties of normal matrices, including spectral characterization, unitary diagonalization, and trace (in)equality through majorization. It highlights equivalent conditions for normality, with...
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Yanfei Xiang (University of Strasbourg)5/18/26, 11:50 AMNumerical Linear Algebra in Machine LearningMinisymposium Talk
This work exclusively focuses on the mixed precision algorithms that integrate classical numerical linear algebra methods with nonlinear neural network-based preconditioners to accelerate the solution of some
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parametric Partial Differential Equations (PDEs). Specifically, we consider Krylov subspace methods such as Flexible GMRES (FGMRES) and Flexible FOM (FFOM), combined with nonlinear or... -
Edward Poon5/18/26, 11:50 AM
The spatial numerical range of an operator $T$ on a normed space $(\mathcal{X}, \| \cdot \|)$ is the set $$W(T) = \{f(Tx) : x \in \mathcal{X}, f \in \mathcal{X}^*, \|x\| = \|f\|^d = f(x) = 1\};$$ when $| \cdot |$ is induced by an inner product this coincides with the classical numerical range. We investigate some properties of the spatial numerical range.
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Mirjeta Pasha5/18/26, 11:50 AMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
Rapidly-growing fields such as data science, uncertainty quantification, and machine learning rely on fast and accurate methods for inverse problems. Three emerging challenges on obtaining relevant solutions to large-scale and data-intensive inverse problems are ill-posedness of the problem, large dimensionality of the parameters, and the complexity of the model constraints. To overcome large...
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Mohammadhossein Mohammadisiahroudi (Department of Mathematics and Statistics, University of Maryland Baltimore County)5/18/26, 11:50 AM
Quantum linear algebra has emerged as a promising framework for accelerating the solution of fundamental computational problems, including systems of linear equations—a core subroutine in many scientific and engineering tasks. These problems arise prominently in optimization algorithms. In this talk, we discuss the opportunities and challenges associated with integrating quantum linear algebra...
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Antwon Park (University of Kentucky)5/18/26, 11:50 AM
We introduce the family of graphical Hermite simplices and study the Smith normal forms of their matrices of vertex vectors, which is equivalent to studying the group structure of the cokernels for these matrices.
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Our motivation is to study the behavior of lattice simplices subject to small lattice perturbations of their vertices.
In this case, a graphical Hermite simplex is a perturbation... -
Dr Mattia Manucci (Karlsruhe Institute of Technology)5/18/26, 11:50 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
In this talk, we present an efficient strategy to approximate the solutions of large-scale generalized Lyapunov equations (GLEs) while providing rigorous error guarantees. The motivation for this study stems from the use of GLEs in model order reduction (MOR) of switched linear systems (SLS) in control form. Specifically, we analyze how inaccuracies in the computed GLE solution influence the...
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Eric Phipps (Sandia National Laboratories)5/18/26, 11:50 AMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP (GCP) method was introduced by Hong, Kolda and Duersch (2020) to allow for flexible choice of the loss function in the optimization problem defining the CP model, enabling more interpretable decompositions of strongly non-Gaussian data such...
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Megan Wawro (Virginia Tech), David Plaxco (University of Georgia)5/18/26, 11:50 AM
The Inquiry-Oriented Linear Algebra (IOLA) project is a research-based, student-centered approach to the teaching and learning of introductory linear algebra. The IOLA curricular materials build from a set of experientially real tasks that allow for active student engagement in the guided reinvention of key mathematical ideas through student and instructor inquiry. The online instructional...
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Julian Mangott (Universität Innsbruck)5/18/26, 2:00 PMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
The development of new drugs and therapies increasingly relies on the numerical simulation of the reaction networks inside biological cells. However, the most accurate description of such reaction networks with the chemical master equation (CME) suffers from the curse of dimensionality, meaning that memory and computational cost grow exponentially with the number of dimensions. This renders...
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Dr Ritesh Khan5/18/26, 2:00 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Hierarchical matrices or $\mathcal{H}$-matrices are the block low-rank representation of the original matrices and are widely used in fast matrix computations. In this talk, we show that the low-rank blocks of $\mathcal{H}$-matrices can be represented in low precision (precision lower than the working precision) without degrading the overall approximation quality. We provide an explicit rule...
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Agnieszka Miedlar (Virginia Tech)5/18/26, 2:00 PM
This talk surveys modern iterative algorithms for solving large-scale nonlinear eigenvector problems, with a focus on both foundational methods and recent advances in nonlinear acceleration techniques. We examine SCF, FEAST, BPSD, and the LOBPCG eigenvector problems solvers, highlighting their theoretical foundations, practical performance, and applications. Through comparisons and...
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Joel Louwsma (Niagara University)5/18/26, 2:00 PM
Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors of the critical group of an arithmetical structure on a graph. We also show that, under suitable hypotheses, critical groups are additive under wedge sums of graphs with arithmetical structures. These results allow...
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Prof. Ken Duffy (Northeastern University)5/18/26, 2:00 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
The study of error correcting codes has two important facets: code construction and decoder design. Many graph-based code constructions have been established to have desirable theoretical properties, but, heretofore, have not been practically decodable. In this talk, we explain recent developments in code-agnostic decoders, including soft-input soft-output variants, that offer a way forward in...
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Dona Ishara Saparamadu (Baylor University, Waco, Texas)5/18/26, 2:00 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
Krylov methods are given for rank-one updates of both eigenvalue and linear equations problems. For eigenvalues, an Arnoldi iteration for the original matrix can be continued on the rank-one changed matrix. We discuss how careful implementation allows the desired accuracy to be attained for the updated matrix. Next, methods are given for linear equations, one that uses the updated Arnoldi...
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Petar Mlinarić (University of Zagreb)5/18/26, 2:00 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Vector fitting is a widely used method for least-squares rational approximation that approaches the nonlinear least-squares problem with a sequence of linear least-squares problems. By contrast, the iterative rational Krylov algorithm (IRKA) is a method for a continuous least-squares approximation, originally formulated as a fixed-point iteration and with a recent interpretation as a...
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Adam Byrne (Trinity College Dublin & IBM Research)5/18/26, 2:00 PM
Quantum subspace diagonalization methods have emerged as a promising application of quantum computers. For matrices $A$ of suitable structure, the unitary operation $U = e^{\imath A t}$ can be efficiently approximated on current quantum devices. This has motivated the use of Krylov subspaces
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$$
\begin{equation}
\mathcal{K}_m=\text{span} \left{\mathbf{x},U\mathbf{x}, ..., U^{m-1}... -
Paul Cazeaux (Virginia Tech)5/18/26, 2:00 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
The Tensor-Train (TT) or Matrix-Product States (MPS) format provides a compact, low-rank representation for high-dimensional tensors, widely used in many-body quantum physics and quantum chemistry. Its efficiency relies on rounding, which reduces tensor ranks to maintain feasible computational costs.
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In this talk, we introduce a novel block-structured randomized sketch exploiting the TT... -
Roberto C. Díaz (Universidad Católica del Norte)5/18/26, 2:00 PM
Let $G$ be a graph with adjacency matrix $A(G)$ and degree matrix $D(G)$. For $\alpha\in[0,1]$, define
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$$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G). $$ Let $\alpha_0$ denote the smallest value of $\alpha$ for which $A_{\alpha}(G)$ is positive semidefinite. It is known that $\alpha_0\le \tfrac12$. For a graph $G$ of order $n$, let $$
\lambda_1(A_{\alpha}(G))\ge \cdots \ge... -
Rute Lemos (CIDMA, University of Aveiro, Portugal)5/18/26, 2:00 PM
The higher rank numerical range is investigated for 2-by-2 block matrices with associated Kippenhahn curves consisting of ellipses and eventually points. As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky et al.
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John Peca-Medlin (UCSD)5/18/26, 2:00 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Gaussian elimination with partial pivoting (GEPP) remains the most widely used dense linear solver. GEPP produces the factorization $PA = LU$, where $L$ and $U$ are lower and upper triangular matrices and $P$ is a permutation matrix; together, these encode the pivoting strategy, directly influencing stability through classical growth-factor bounds and matrix norm inequalities. When $A$ is...
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Tim Mitchell (CUNY Queens College & The Graduate Center)5/18/26, 2:00 PM
In this talk, we consider computing the worst-case (highest) $\mathcal{H}_\infty$ norm of a either a continuous-time or discrete-time linear time-invariant parametric system, where the state-space matrices all depend on a single real-valued scalar parameter $\mathsf{p}$ on a domain $\mathcal{P}$ consisting of a finite number of intervals. On each interval in $\mathcal{P}$, we assume that...
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James Hazelden (University of Washington)5/18/26, 2:00 PMNumerical Linear Algebra in Machine LearningMinisymposium Talk
How are learned representations incrementally formed to solve tasks by Gradient Descent (GD)? In this talk, we will show that each step of GD is exactly given by the application of a massive tensor-valued linear operator, which we call the Configuration Space Neural Tangent Kernel (NTK). We prove that it can be decomposed into two operators: P and K, the former capturing state-to-state...
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Rudi Smith (Virginia Tech)5/18/26, 2:25 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Continuous-time algebraic Lyapunov equations are linear matrix equations of the form
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$$ \begin{equation*} A X E^{\mathsf{H}} + E X A^{\mathsf{H}} = -W \end{equation*} $$ where $A, E \in \mathbb{C}^{n \times n}$ are large-scale sparse coefficient matrices and $W = B R B^{\mathsf{H}}$ represents an indefinite right-hand side defined by the low-rank factor $B \in \mathbb{C}^{n \times... -
Xinye Chen (LIP6, CNRS, Sorbonne University)5/18/26, 2:25 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Achieving optimal performance in numerical computations often hinges on aggressively reducing precision or performing rigorous rounding-error analysis to retain numerical accuracy. The precision tuning methods provide a unified, task-specific validation platform for automated precision tuning, enabling a balance between computational efficiency and numerical fidelity. In this talk, we present...
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Jordan Jackson (Virginia Tech)5/18/26, 2:25 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
Many applications require the solution of large-scale linear systems that have nonlinear parameter dependence. The Infinite GMRES algorithm, developed by Jarlebring and Correnty in 2022, converts these systems into infinite-dimensional systems with linear parameter dependence. This transformation involves a linearization process that results in a system with a special companion-like structure....
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Froilán M. Dopico (Universidad Carlos III de Madrid (Spain))5/18/26, 2:25 PM
We propose an algorithm that approximates a given matrix polynomial of any degree $d$ by another matrix polynomial of a prescribed rank and degree at most $d$. The algorithm combines recent advances in the theory of generic factorizations for matrix polynomials of bounded rank and degree with an alternating least squares strategy. For $d=1$, the algorithm includes the important case of matrix...
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Natalia Bebiano (Department of Mathematics of the University of Coimbra, Portugal)5/18/26, 2:25 PM
The Kippenhahn curve associated to generalized Kac-Sylvester matrices are characterized for matrices of order less than 10. The corresponding higher rank-numerical ranges are determined. Based on computational evidence, we conjecture the types of algebraic curves that may appear for an arbitrary order.
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Zhanrui Zhang (University of Illinois Urbana-Champaign)5/18/26, 2:25 PMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
The Canonical Polyadic (CP) decomposition is widely used to represent high-dimensional data in many applications, for example, solving high-dimensional PDEs like kinetic equations. A key challenge in these problems is the efficient estimation and reduction of the CP rank. The CP rank reduction task can be formulated as approximating the Khatri–Rao product of the CP factor matrices with a lower...
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Shuxing Li (University of Delaware)5/18/26, 2:25 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Determining the minimum Hamming distance of an error-correcting code $\mathcal{C}$ has long stood as a fundamental challenge in coding theory. In this talk, we turn our attention to an even more ambitious problem: determining the full Hamming weight distribution of $\mathcal{C}$. This means counting the number of codewords in $\mathcal{C}$ of each possible Hamming weight—an essential but...
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Jessie Chen (North Carolina State University)5/18/26, 2:25 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
Gaussian process regression uses data measured at sensor locations to reconstruct a spatially dependent function with quantified uncertainty. However, if only a limited number of sensors can be deployed, it is important to determine how to optimally place the sensors to minimize a measure of the uncertainty in the reconstruction. We consider the Bayesian D-optimal criterion to determine the...
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Haoran Ni (University of Warwick)5/18/26, 2:25 PMNumerical Linear Algebra in Machine LearningMinisymposium Talk
Normalizing Flows (NFs) enable tractable density evaluation by modelling data through invertible neural transformations. However, this reliance on global bijectivity severely restricts their expressiveness when the target distribution lies on a low-dimensional manifold or exhibits complex topology. To overcome this limitation, we introduce Principal Surjective Flows (PSFs), a framework that...
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Ryan LaRose5/18/26, 2:25 PM
Quantum Krylov methods are strong candidates for computing ground states on NISQ and MegaQuop computers. While typically implemented with powers of the time evolution unitary $e^{-iH t}$ for a given Hamiltonian $H$, convergence can be markedly faster with powers of the Hamiltonian $H$ itself as in classical methods. We discuss these convergence rates and present several ways to implement...
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Ms Swagata Dutta (Indian Institute of Technology Kharagpur)5/18/26, 2:25 PM
The permanent of a matrix plays a fundamental role in combinatorics and graph theory, yet its exact computation is difficult. This difficulty has motivated extensive research on upper and lower bounds for the permanent under various graph constraints. In this paper we investigate some permanental bounds of bicyclic graphs in which the two cycles intersect each other. We establish sharp lower...
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Mohsen Aliabadi (Clayton State University)5/18/26, 2:25 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We survey classical results in additive combinatorics and develop linear analogues over field extensions, with an emphasis on Kneser-type phenomena. In addition to recalling Kneser's theorem and stabilizer methods (including Cauchy--Davenport and DeVos's refinement), we present a rigidity theorem showing that if $|A+B|=|A|+|B|-1$ with $A+B\neq G$, then $A+B$ is a subgroup and $A$ is a coset;...
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Michael Jones5/18/26, 2:25 PM
The two-level orthogonal Arnoldi algorithm, abbreviated as TOAR, proposed by Lu, Su and Bai, is a Krylov method for the solution of large sparse quadratic eigenvalue problems (QEPs). Traditionally, such eigenproblems are first linearised with an appropriate companion form, then fed into the standard Arnoldi algorithm. This approach has the advantage of being simple, but suffers from large...
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Dr Carlos Alfaro (Banxico)5/18/26, 2:25 PM
Graham, Lovász and Pollak obtained a well known formula for the determinant of distance matrices of trees. This formula depends only on the number of vertices of the tree and not on its topological structure. Later, Hou and Woo computed the explicit expression of the Smith form of the distance matrix of a tree, which again, it depends only on the number of vertices. In this talk, we will show...
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Raf Vandebril (Dept. Computer Science, KU Leuven)5/18/26, 2:50 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
A major problem for time series clustering is that computing the similarity matrix for the most used similarity measures becomes infeasible if number amount or length of time series becomes too large. However, since this similarity matrix typically has low-rank structure, it can be approximated using a low-rank approximation. In this work, we show that existing numerical linear algebra...
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Marko Orel (University of Primorska)5/18/26, 2:50 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The matrix equation $rank(A-B)=1$ is well studied in linear algebra and combinatorics within preserver problems and the theory of distance-regular graphs/association schemes. In the talk I will present how this equality is related to coding theory, namely to binary self-dual codes.
Let $\widehat{\Gamma}_{n}$ be the graph with the vertex set formed by all $n\times n$ symmetric...
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Ralihe Raul Villagran Olivas (Worcester Polytechnic Institute)5/18/26, 2:50 PM
Chip-firing is a discrete dynamical process on a graph that exhibits striking phenomena, including fractal-like symmetries and self-organized criticality. From an algebraic perspective, the states of this process (combinatorially) define a group, the Sandpile group, whose algebraic structure is given by the Smith normal form of the Laplacian matrix. We will discuss problems related to Sandpile...
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Dr Kathryn Haymaker (Villanova University)5/18/26, 2:50 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
In this talk, we present a family of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon and polynomial evaluation codes using a construction of superimposed codes by Kautz and Singleton. Using a novel ordering of the codewords and evaluation points, we show both the number of levels in the hierarchy and the index of these $q$-ary-derived codes...
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Daniel Bielich (Synopsys)5/18/26, 2:50 PM
LS-DYNA is a multiphysics simulation software package. It targets a wide range of industrial applications, such as modal analysis problems. These are solved with a variety of homegrown eigensolvers, tailored over decades to industrial models. In this talk, we will focus our attention on the quadratic eigenvalue problem underlying the rotational dynamics' framework of the Jeffcott Rotor model....
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Polina Sachsenmaier (RWTH Aachen University)5/18/26, 2:50 PMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
Standard numerical methods for solving PDEs typically suffer from the curse of dimensionality: their computational cost scales exponentially with the dimension of the underlying domain, making them impractical even at low resolution. In many cases of interest, however, such limitations can be overcome by appropriately compressed representations of approximate solutions, for example, by...
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Takeshi Terao (Waseda University)5/18/26, 2:50 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
We consider the eigenvalue problem $Ax^{(i)} = \lambda_i x^{(i)}$ for a real symmetric matrix $A \in \mathbb{R}^{n \times n}$, where $\lambda_i \in \mathbb{R}$ is an eigenvalue of $A$ and $x^{(i)} \in \mathbb{R}^n$ is the corresponding eigenvector. This work investigates iterative refinement methods to improve the accuracy of eigenvectors $x^{(i)}$.
Efficient methods are known for improving...
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Linda Patton (Cal Poly San Luis Obispo)5/18/26, 2:50 PM
Using results from Brown-Halmos, Klein (1972) described the numerical range of a general Toeplitz operator on $H^2(\mathbb{D})$. In particular, the numerical range of a Toeplitz operator $T_p$ with polynomial symbol $p$ is the convex hull of the image of the unit disk under $p$. By analyzing $p(\mathbb{T})$ and its relationship to the Kippenhahn curve of a matrix, we provide conditions under...
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Peter Semrl (Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia)5/18/26, 2:50 PM
The general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on projective geometry which works also in the real case.
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Sam Bender5/18/26, 2:50 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
We consider single-input, single-output systems with time-varying, periodic parameters:
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ẋ(t) = A(t)x(t) + b(t)u(t),
y(t) = c(t) x(t),
where A(t) ∈ ℝⁿˣⁿ and b(t), c(t) ∈ ℝⁿ all have period T.
Such systems arise when modeling phenomena in fluid dynamics, structural mechanics, and electronic circuits. In particular, linearization around known periodic orbits of a nonlinear model produces a... -
Eda Oktay (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)5/18/26, 2:50 PMNumerical Linear Algebra in Machine LearningMinisymposium Talk
As machine learning and AI continue to shape modern hardware design, reduced-precision arithmetic has become essential in high-performance computing. Recent advances in hardware architectures—such as AI accelerators, GPUs, and tensor-core technologies—many of which are driven by machine-learning workloads, are optimized for low-precision operations to improve performance and reduce energy...
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Daan Camps (Lawrence Berkeley National Laboratory)5/18/26, 2:50 PM
Randomized quantum algorithms for linear systems problems have attracted attention as potential candidates for early fault-tolerant quantum computers due to their potentially shallower circuit depths compared to block encoding-based methods. However, questions remain about whether they can offer practical advantages in near-term applications. We present a comprehensive resource analysis of a...
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Anshul Prajapati (Max Planck Institute for Dynamics of Complex Technical Systems)5/18/26, 2:50 PM
We study linear time-invariant Dissipative Hamiltonian (DH) systems arising in energy-based modeling of dynamical systems. An advantage of DH systems is that they are always stable due to the structure of their coefficient matrices, and, under further weak conditions, even asymptotically stable. Here, we consider the computation of the stability radii for a given asymptotically stable DH...
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Abigail Williams (Baylor University)5/18/26, 2:50 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
A very simple approach to solving multiple right-hand side systems is proposed. For symmetric problems, the conjugate gradient method is a very efficient way to solve linear equations. We will use the same parameters from solving the first system for other systems. This is called Twin CG. It corresponds to applying the same polynomial to the other systems as was used for the first system. No...
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Mykhailo Kuian (Case Western Reserve University)5/18/26, 3:45 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
We consider the numerical solution of linear operator equations involving compact operators. Since compact operators do not admit bounded inverses, the associated equations are ill-posed and require regularization. The Arnoldi process provides a natural framework for approximating a compact operator by a nearby operator of finite rank, thereby reducing the infinite-dimensional problem to a...
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Zhuoyao Zeng (University of Stuttgart, Germany)5/18/26, 3:45 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
We address the issue of an efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix.
For this aim, we rely on projection-based model order reduction (MOR), i.e., we approximate the large-scale problem by projecting it onto a suitable subspace and reducing it to a problem of a much smaller dimension....
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Ilse Ipsen (North Carolina State University)5/18/26, 3:45 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
It is well known that the problem of selecting k columns with maximal volume from a real matrix is NP-hard, and does not admit a polynomial time approximation scheme. However, one can show that the logarithm of the volume is a "submodular" function. Intuitively, this means: Adding a new column to a larger submatrix tends to be less beneficial than adding it to a smaller submatrix.
If subset...
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Dr Xianqi Li (Florida Institute of Technology)5/18/26, 3:45 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
Magnetic Resonance Imaging (MRI) is a critical tool in modern medical diagnostics, yet its prolonged acquisition time remains a critical limitation, especially in time-sensitive clinical scenarios. While undersampling strategies can accelerate image acquisition, they often result in image artifacts and degraded quality. Recent diffusion models have shown promise for reconstructing...
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Muhammad Faisal Khan (University of Insubria)5/18/26, 3:45 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the ill-posedness. The equation involves a Caputo fractional derivative in the space variable and a tempered fractional derivative in the time variable, both of...
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David S Watkins (Washington State University)5/18/26, 3:45 PM
Periodic CMV matrices are unitary matrices that can be specified by $O(n)$ data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using $O(n^{2})$ data) in $O(n^{3})$ time. Since periodic CMV matrices can be specified by $O(n)$ data, one would hope to find a method that computes the eigenvalues in $O(n^{2})$ time instead of $O(n^3)$. This is indeed...
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Prof. Conrad Plaut (University of Tennessee--Mathematics)5/18/26, 3:45 PM
Modern technology is most often employed in two ways in math education: to enhance explanations (e.g. animated videos or widgets), or to find solutions and calculate answers. The fact that students sometimes do poorly even when taught by excellent teachers shows the limitations of the first strategy. The second strategy, which has been made incredibly easy by generative AI, is increasingly...
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Andrew Horning (Rensselaer Polytechnic Institute)5/18/26, 3:45 PMTheoretical Advances in Operator LearningMinisymposium Talk
Linear operators with a continuous spectrum often lurk behind complex physical phenomena in nature, from wave attractors in geometrically confined fluids to topological bifurcations in dynamical systems. However, they are notoriously tricky to learn from data. For example, finite-dimensional approximations of the operator must “discretize” the continuous spectrum into finitely many points and...
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Liron Mor Yosef (Tel Aviv University)5/18/26, 3:45 PM
The emergence of Quantum Numerical Linear Algebra (qNLA) offers a paradigm shift in solving large-scale linear systems and matrix functions. However, the practical utility of these algorithms, such as the seminal HHL, is fundamentally bottlenecked by the "input problem", namely the efficient representation of classical matrices as quantum circuits.
In this talk, we explore two distinct...
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Gianfranco Verzella (University of Geneva)5/18/26, 3:45 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
In this work, we present the tree tensor network Nyström (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker or tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nyström approximation for matrices, i.e. it is...
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Daisuke Hirota (National Institute of Technology, Tsuruoka College)5/18/26, 3:45 PM
The Cauchy functional equation plays a fundamental role in the study of additive and linear structures arising from numerical and norm-related information in functional analysis. In this talk, we investigate preserver problems on positive cones of commutative C$^{*}$-algebras, where a norm identity of Fischer--Muszély type, arising from the Cauchy functional equation, determines the underlying...
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Leslie Hogben (American Institute of Mathematics, Iowa State University, Purdue University)5/18/26, 3:45 PM
The graph ${\mathcal G}(A)$ of a real symmetric matrix $n\times n$ matrix $A=[a_{ij}]$ has vertices $V=\{1,\dots,n\}$ and edges $E=\{ \{i,j\}: a_{ij}\ne 0\mbox{ and } i\ne j\}$. The set of matrices described by a graph $G$ is ${\mathcal S}(G)=\{A\in{\mathbb R}^{n\times n}:{\mathcal G}(A)=G \mbox{ and } A^\top=A\}$ and the
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Inverse Eigenvalue Problem of $G$ (IEP-$G$) is to determine all... -
Wei Gao5/18/26, 3:45 PM
Let $G$ be a simple connected graph. A vertex-degree-based topological index is defined as $$TI_f(G) = \sum_{uv \in E(G)} f(d_u, d_v),$$ where $f(x, y)$ is a symmetric real function. In theoretical chemistry, these indices serve as essential numerical molecular descriptors in QSAR/QSPR models. In this work, we investigate the extremal properties of $TI_f + RTI_f$, defined as the sum of a...
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Till Peters (TU Braunschweig, Institute for Numerical Analysis)5/18/26, 4:10 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Today, mathematical modeling is dominated by increasingly high-dimensional and complex dynamical systems. One special type of structure is the bilinear state equation, which either naturally appears in various applications or results from the Carleman bilinearization of the underlying nonlinear dynamics. Recently, dynamical systems with quadratic outputs have also gained significant attention...
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Nik Stopar (University of Ljubljana)5/18/26, 4:10 PM
In this talk we demonstrate how a matrix algebra over a finite field can be completely described using combinatorial properties. The main tool that allows one to do this is the compressed zero-divisor graph of a ring, which describes pairs of matrices $A$ and $B$ such that $AB=0$. We list a set of $5$ combinatorial axioms that uniquely determine the compressed zero-divisor graph...
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Gianna M. Del Corso (Dip. Informtica, Università di Pisa)5/18/26, 4:10 PM
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, providing an embedding of a given matrix into a suitable larger unitary matrix. Efficient techniques for QBE have primarily focused on sparse matrices, and less effort has been devoted to data-sparse matrices, such as rank-structured matrices.
In this talk, we examine a specific case of rank...
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Jeffrey Stuart (Pacific Lutheran University)5/18/26, 4:10 PM
Traditionally, half or more of a first course in linear algebra has been devoted to the theory and machinery required to solve linear systems and to find bases for the four fundamental subspaces associated with a matrix. At the heart of this is the Gauss-Jordan algorithm, used to construct the reduced row echelon form (RREF) of a matrix. Far too many students complete their only linear algebra...
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Nancy Menzelthe (University of Nevada, Reno)5/18/26, 4:10 PM
Given $1\le k\le n$, the $k$-numerical range of $A\in \mathbb{C}_{n\times n}$ is defined by
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$$ W_k(A): = \left\{ \sum_{i=1}^k x_i^*Ax_i: x_1, \dots, x_k\ \mbox {orthonormal vectors in } \mathbb{C}^n\right\}\subset \mathbb{C}. $$ Motivated by Davis' intuitive explanation of the Elliptical Range Theorem, we introduce two notions of multiplicity for points in $W_k(A)$, namely wedge... -
Michael Overton (New York University)5/18/26, 4:10 PM
It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this talk we point out that when the "wrong" choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.
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Hayden Henson (Baylor University)5/18/26, 4:10 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
Preconditioning plays a central role in accelerating the convergence of iterative methods for solving large linear systems. Among the various approaches, polynomial preconditioning offers a flexible approach. Krylov subspace methods provide a natural setting for constructing polynomials that can be used as preconditioners. In this work, we investigate the use of polynomial preconditioning...
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Toluwani Okunola (Tufts University)5/18/26, 4:10 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Many imaging inverse problems assume a known linear forward operator, yet practical systems often suffer from uncertainty in acquisition geometry, such as projection angles in computed tomography, sensor positions in photoacoustic tomography. These uncertainties introduce nonlinearity and require joint estimation of both the image and the forward model parameters.
We propose a nonlinear...
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Dimitrios Giannakis (Dartmouth College)5/18/26, 4:10 PMTheoretical Advances in Operator LearningMinisymposium Talk
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for analysis and modeling of nonlinear dynamical systems, and has received considerable interest over the years from mathematical, computational, and domain-scientific...
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Subhayan Saha (Universite de Mons)5/18/26, 4:10 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise...
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Daniela Calvetti (Case Western Reserve University)5/18/26, 4:10 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
Many computational problems involve solving a linear system of equations, although only a subset of the entries of the solution are needed. In inverse problems, where the goal is to estimate unknown parameters from indirect noisy observations, it is not uncommon that the forward model linking the observed variables to the unknowns depends on variables that are not of primary interest, often...
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Cameron Musco (University of Massachusetts Amherst)5/18/26, 4:10 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
In this talk, I will give an overview of recent progress on the problem of structured matrix approximation from matrix-vector products. Given a target matrix A that can only be accessed through a limited number of (possibly adaptively chosen) matrix-vector products, we seek to find a near-optimal approximation to A from some structured matrix class – e.g., a low-rank approximation, a...
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Brendan Rooney (Rochester Institute of Technology)5/18/26, 4:10 PM
Given a graph $G$ on $n$ vertices, $\mathcal{S}(G)$ is the set of symmetric $n\times n$ matrices with the same off-diagonal zero pattern as the adjacency matrix $A(G)$. We say that a graph $G$ has $q(G)=2$ if there is a matrix $M\in \mathcal{S}(G)$ with exactly $2$ distinct eigenvalues. This is equivalent to the existence of an orthogonal matrix $M\in\mathcal{S}(G)$. We are interested in...
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LUIZ EMILIO ALLEM (Universidade Federal do Rio Grande do Sul)5/18/26, 4:35 PM
We study the minimum number of distinct eigenvalues $q(G)$ of threshold graphs. It is known that every threshold graph satisfies $q(G)\leq 4$, which suggests that a complete combinatorial characterization according to the values $q(G)=2,3,4$ is possible.
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In this talk, we present ongoing results toward such a characterization. -
Oshani Jayawardane (Embry-Riddle Aeronautical University)5/18/26, 4:35 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
Code Recovery using algebraic-geometric approaches becomes computationally expensive with the cardinality of the field and the complexity of the code structures. In response, we present a low-complexity algorithm that utilizes structures in algebraic-geometric codes over finite fields. The low-complexity algorithm recovers algebraic codes over finite fields locally, which we name as lrc...
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Martijn Boussé (Maastricht University)5/18/26, 4:35 PM
Linear Algebra is a core mathematics course in numerous undergraduate programs, yet students often struggle with its abstract nature and with recognizing key connections between topics. This lack of conceptual coherence motivates the need for innovative teaching approaches that make linear algebra more accessible, engaging, and meaningful.
We developed a Linear Algebra card game grounded in...
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Roel Van Beeumen (Lawrence Berkeley National Laboratory)5/18/26, 4:35 PM
With the Quantum Singular Value Transformation (QSVT) emerging as a unifying framework for diverse quantum speedups, the efficient construction of block encodings—their fundamental input model—has become increasingly crucial. However, devising explicit block encoding circuits remains a significant challenge. A widely adopted strategy is the Linear Combination of Unitaries (LCU) method. While...
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Reetish Padhi (Virginia Tech)5/18/26, 4:35 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
We develop the theoretical framework for extending the quadrature based balanced truncation (QuadBT) method to linear systems with quadratic outputs (LQO). QuadBT which was originally designed for data-driven balanced truncation of standard linear systems with linear outputs only. We show that by sampling the extended impulse responses (kernels) and their derivatives (in the time domain) or...
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John Urschel (MIT)5/18/26, 4:35 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
The discrete Fourier transform matrix, and sub-matrices of it, appear in a wide variety of applications. While the Fourier matrix itself is a scaled unitary matrix, its sub-matrices can be exponentially ill-conditioned. In this talk, we discuss applications, prior work, and we provide tight estimates for just how ill-conditioned such matrices can be.
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Riley Yizhou Chen (Emory University)5/18/26, 4:35 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Learning solution operators in a manner that is independent of discretization and resolution remains a central challenge in data-driven modeling. The latent twins framework addresses this problem by constructing operators in a task-adaptive latent space for inverse problems and differential equations. However, in its classical form, latent twins relies on autoencoder architectures that are...
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Bohan Chen (California Institute of Technology)5/18/26, 4:35 PMTheoretical Advances in Operator LearningMinisymposium Talk
Many classic methods in data assimilation, like the Ensemble Kalman Filter (EnKF), are limited by its Gaussian ansatz. In this work, we frame the filtering update as learning a nonlinear operator mapping between probability distributions in the mean-field limit. We introduce Measure Neural Mappings (MNMs), a class of neural operators acting on probability measures, implemented via Set...
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Stefano Sicilia (University of Mons)5/18/26, 4:35 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Given a matrix $X$, and two ranks $r_1$ and $r_2$, the Hadamard decomposition (HD) consists in looking for two low-rank matrices, $X_1$ of rank $r_1$ and $X_2$ of rank $r_2$, both of the same size as $X$, such that $X\approx X_1\circ X_2$, where $\circ$ is the Hadamard (element-wise) product. HD is more expressive than standard low-rank approximations, such as the truncated singular value...
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Brooke Randell (UCSC)5/18/26, 4:35 PM
In 2022, Hwa-Long Gau and Pei Yuan Wu discussed the numerical range of various Hankel matrices with an emphasis on which subsets of the complex plane are attainable. We will be discussing as well as expanding upon these results when the Hankel matrices are positive and Hermitian.
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Achintya Sunil5/18/26, 4:35 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
Design problems such as topology optimization and PDE-based inverse problems require the solution of a sequence of linear-systems derived from finite element or finite difference discretization. Preconditioning is essential for the fast solution of these systems by iterative methods. However, computing an accurate preconditioner for every system in the sequence may be a computational...
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Victor Pan (City University of New York)5/18/26, 4:35 PM
Low Rank Approximation (LRA) of a matrix are invaluable for Numerical Linear Algebra and Data Science. Some recent papers propose superfast algorithms that output LRAs with near-optimal accuracy for a large class of inputs but, as ANY superfast LRA algorithm, fail on a large class of inputs as well. To narrow the latter class we first superfast compute a crude initial LRA by applying one of...
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Chris Hart (Georgia State University)5/18/26, 4:35 PM
Let $A$ be an $m \times n$ real matrix. If the manifolds ${\widetilde{\cal M}_A}= \{ H^{-1} A G : G, H \text{ are nonsingular} \}$ and $Q(\text{sgn}(A))$ intersect transversally at $A,$ that is, the tangent spaces of ${\widetilde{\cal M}_A}$ and $Q(\text{sgn}(A))$ at $A$ sum to $ \mathbb R ^{m\times n},$ we say that $A$ has the rank-preserving transversality property (RPTP) and that $A$ is an...
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Vasilije Perovic (University of Rhode Island)5/18/26, 5:00 PMLow-Complexity Data-driven or Classical Algorithms and ApplicationsMinisymposium Talk
In this talk we discuss various computational aspects of determining all singular triplets $\{\sigma_j, u_j, v_j\}$ corresponding to singular values of $A$ above a user-specified threshold parameter $sigma$, or in other words, determining a $k$-PSVD of $A$ such that $\sigma_k \geq sigma$ and $\sigma_{k+1} < sigma$. While various numerical schemes with publicly available software have been...
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Polona Oblak (University of Ljubljana)5/18/26, 5:00 PM
For a tree $T$ we consider the set ${\mathcal S}(T)$ of real symmetric matrices whose off-diagonal zero-nonzero pattern is equal to the pattern of the adjacency matrix of $T$. It is well known that the maximum multiplicity of an eigenvalue over matrices in ${\mathcal S}(T)$ is equal to the path cover number $P(T)$ of the tree $T$.
We present a novel decomposition of the tree into a set of...
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Stefan Güttel (The University of Manchester)5/18/26, 5:00 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
Randomized sketching is a promising tool to reduce the number of inner products computed in Krylov methods for solving large systems of linear equations $Ax = b$, or more generally, when approximating the action of a matrix function on a vector, $f(A)b$. For the case of linear systems, it has recently been observed that one can often get away with completely inner product-free Krylov-based...
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Serkan Gugercin (Virginia Tech)5/18/26, 5:00 PMTheoretical Advances in Operator LearningMinisymposium Talk
We introduce a unified approach to $\mathcal{L}_2$-optimal reduced-order modeling that applies to both linear time-invariant dynamical systems and stationary parametric problems. The framework leverages parameter-separable representations to obtain gradient information for the $\mathcal{L}_2$ objective with respect to the reduced operators, enabling a fully nonintrusive, data-driven,...
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Dr Malena Sabate Landman (University of Bath)5/18/26, 5:00 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
This talk presents a new family of algorithms for large-scale linear inverse problems built on flexible and inexact variants of the Golub–Kahan factorization. The proposed approach constructs regularized solutions through a sequence of projected (re)weighted least-squares problems, where the projection spaces are adaptively generated and endowed with iteration-dependent preconditioning and...
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Cade Ballew (University of Washington)5/18/26, 5:00 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
The Akhiezer iteration is a new iterative method for solving indefinite linear systems and computing matrix functions. The iteration uses orthogonal polynomial recurrence coefficients to efficiently compute the action of a matrix polynomial to a vector without computing inner products. It features an a priori computable convergence rate and is often faster in practice than standard Krylov...
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Kennett Dela Rosa (University of the Philippines Diliman)5/18/26, 5:00 PM
This study considers some problems involving the $k$-numerical range. Following the idea of the zero-dilation index, the notion of the zero-trace index is introduced, which is defined as the largest zero-trace compression of a matrix. Alternative characterization of the zero-trace index is given, and zero-trace indices of certain classes of matrices are identified. The study also considers...
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Johnna Parenteau5/18/26, 5:00 PM
Given a simple graph, $G$, on $n$ vertices, let $S(G)$ be the set of $n \times n$ real symmetric matrices, $A = [a_{ij}]$, associated to $G$ where, when $i\neq j$, $a_{ij} \neq 0$ if and only if $ij$ is an edge in $G$ and the main diagonal is free to be chosen. For any square matrix, $A$, let $q(A)$ equal the number of distinct eigenvalues of $A$. The minimum number of distinct eigenvalues of...
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Kingsley Michael (Baylor University)5/18/26, 5:00 PMKrylov Iterative Methods for Linear EquationsMinisymposium Talk
Golub-Kahan bidiagonalization procedure is well known for its role in computing singular values and solving least squares problems. We present a polynomial-preconditioned variant of this framework aimed at reducing the need for restarting and extensive orthogonalization. This talk outlines the formulation and motivation for the method and examines its potential to improve performance in...
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Filippo Della Chiara (KU Leuven)5/18/26, 5:00 PM
Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through “block encodings”, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum...
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Soo Go (City University of New York)5/18/26, 5:00 PM
A matrix algorithm is said to be superfast (aka runs at sublinear cost) if it involves much fewer scalars and flops than an input matrix has entries. Such algorithms have been extensively studied and widely applied in modern computations for matrices with low displacement rank and more recently for low rank approximation of matrices, even though any superfast algorithm fails on worst case...
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Damjana Kokol Bukovšek (University of Ljubljana)5/18/26, 5:00 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
We consider a symmetric nonnegative matrix $A$ of order $n \times n$. A factorization of the form $A = BCB^T$, where $B$ is a nonnegative matrix of order $n \times k$ and $C$ is a symmetric nonnegative matrix of order $k \times k$, is called symmetric nonnegative trifactorization (SNT for short) of $A$. Minimal possible $k$ in such factorization is called the SNT-rank of $A$.
The...
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5/19/26, 8:20 AMPlenary Talk
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Arvind Krishna Saibaba (North Carolina State University)5/19/26, 8:30 AM
Estimating the trace of a matrix, that is only accessible by matrix-vector products, is a fundamental task in scientific computing and data science. This has many applications including network analysis, estimation of matrix norms and spectral densities, estimation of log-determinants, etc. Monte Carlo methods is one of the prevalent approaches for estimating the trace of the matrix. We...
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Jephian C.-H. Lin (National Yang Ming Chiao Tung University)5/19/26, 9:25 AM
Inverse problems on a graph investigate how spectral behaviors interact with the matrices associated with the given graph. Such problems not only uncover structural information about the graph from its spectral data, but also identify fundamental properties shared by all matrices defined on the graph. A classic example is the Colin de Verdière parameter, which characterizes planarity via the...
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Fuzhen Zhang (Nova Southeastern University)5/19/26, 11:00 AM
Linear algebra is fundamental to mathematics and has wide-ranging applications in science, engineering, and data analysis. As a core mathematical subject, it is taught to students at both the high school and college levels, not only in mathematics but also across the sciences. Is linear algebra easy? It may not be as easy as it sounds. Is teaching linear algebra easy? It may not be as easy as...
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Aida Abiad (Eindhoven University of Techonolgy)5/19/26, 11:00 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
A unified framework of the Expander Mixing Lemma for irregular graphs using adjacency eigenvalues will be presented, as well as several new versions of it. We will also show some of its applications in graph theory, which include spectral bounds on the zero forcing number of a graph. To derive our results we use a new application of weight partitions of graphs, where the Perron eigenvector...
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Shuai Shao (The University of Manchester)5/19/26, 11:00 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions exp(−𝑡𝑧) for 𝑧 ≥ 0 and 𝑡 in a positive time interval 𝑇. Our result extends a classical result by J.-E. Andersson [J. Approx. Theory, 32(2):85–95, 1981] on the asymptotic best rational approximation of exp(−𝑧) with real poles. Numerical...
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punit sharma (Indian Institute of Technology Delhi - Abu Dhabi, UAE)5/19/26, 11:00 AM
Let $G, H_1,\ldots,H_s \in \mathbb C^{n,n}$ be Hermitian and $S_1,\ldots,S_k \in \mathbb C^{n,n}$ be symmetric matrices. In this talk, we maximize the Rayleigh quotient of a Hermitian matrix $H$ under certain constraints involving Hermitian matrices $H_1,\ldots, H_s$ and symmetric matrices $S_1,\ldots, S_k$. More specifically, we...
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Dan E. Folescu (Virginia Tech)5/19/26, 11:00 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Modal truncation has long been a fundamental approach of model order reduction: to systematically eliminate eigenmodes of a dynamical system that contribute little to the modeling behavior over a given time/frequency range. Typically, this procedure requires the ability to access and utilize intrusive state-space information about the underlying full-order system, which can be infeasible for...
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Daniel Hayes (University of Delaware)5/19/26, 11:00 AMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
Recently, there have been many advances in the area of randomized and sampling-based methods for data approximation. This has led to significant progress towards the efficient treatment of large data in both compression and utilization in computation. In this talk, I will discuss a current work that uses random oversampling on a Tensor Train Cross (TT-Cross) approximation in order to reduce...
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Yuxin Ma (Charles University)5/19/26, 11:00 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems $Ax = b$, where $A$ is a symmetric positive definite matrix. Rather than computing residuals directly, it updates the residual vectors recursively. Current analyses of the conjugate gradient (CG) algorithm in finite precision typically assume that the norm of the...
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Andreas Mang (Department of Mathematics, University of Houston)5/19/26, 11:00 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
We propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) for accelerating first-order optimization algorithms. The method is applied to preconditioned first-order schemes by interpreting their update rules as fixed-point iterations. GA-NGMRES introduces a periodic mixing strategy that alternates between NGMRES extrapolation and fixed-point updates,...
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Tanvi Jain (Indian Statistical Institute)5/19/26, 11:00 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We discuss majorisation inequalities for different means of positive definite matrices focusing on the geometric mean, the Wasserstein mean, the log Euclidean mean and the power mean.
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Alec Dektor (Lawrence Berkeley National Lab)5/19/26, 11:00 AM
I will present two projection methods for solving high-dimensional tensor eigenvalue problems with low-rank structure: an inexact Lanczos method and an inexact polynomial-filtered subspace iteration. The inexactness arises from low-rank compression, which enables efficient representation of high-dimensional vectors in low-rank tensor formats. A central challenge is that standard operations,...
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Rafael D'Oliveira (Clemson University)5/19/26, 11:00 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Matrix multiplication is, oftentimes, the most expensive computational task in an algorithm. It is the computational bottleneck for training many of the now well-celebrated learning algorithms, for example. To speed up the algorithm, the data can be distributed on many machines to perform the computations in parallel. This sharing of the data, however, raises security concerns when the data is...
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Kate Lorenzen (Linfield University)5/19/26, 11:00 AM
Graphs can be encoded into a matrix according to some rule. The eigenvalues of the matrix are used to understand the structural properties of graphs. If two graphs share a set of eigenvalues, they are called cospectral. A tree is a graph with no cycles, and for most matrix representations, almost all trees have a cospectral mate. The distance Laplacian matrix is found by subtracting the...
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Jonathan Tabares (Florida International University)5/19/26, 11:00 AM
This work presents a quantized tensor train (QTT)-accelerated finite-difference time-domain (FDTD) algorithm for solving Maxwell equations in 3D open domains.
Upon a QTT representation of both field variables and differential operators on uniform grids, the proposed algorithm can achieve up to logarithmic scaling in memory and per-step computational cost with respect to the number of...
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Kathryn Lund (STFC Scientific Computing)5/19/26, 11:00 AMNumerical Linear Algebra in Machine LearningMinisymposium Talk
The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer Linear Algebra Appl 27(3):e2288). In this work, we investigate properties of the Fréchet derivative of the tensor t-function and derive algorithms for its efficient numerical computation. Applications in condition number estimation and nuclear...
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Martin Plávala (Leibniz University Hannover)5/19/26, 11:00 AMConvex Structures in Quantum Information and GravityMinisymposium Talk
The gravity-mediated entanglement experiments employ concepts from quantum information to argue that if entanglement due to gravitational interaction is observed, then gravity cannot be described by a classical system. However, the proposed experiments remain beyond out current technological capability, with optimistic projections placing the experiment outside of short-term future. Here we...
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Chen Greif (The Department of Computer Science)5/19/26, 11:25 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
We consider nonsymmetric double saddle-point systems. Given the 3-by-3 block structure of the matrix, the associated block LU decomposition features two Schur complements. A theoretical question we explore is what happens when one of the Schur complements is inverted exactly and the second, nested one, is approximated. Eigenvalue analysis sheds some light on the effect of this type of...
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Emil Krieger (Bergische Universität Wuppertal)5/19/26, 11:25 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Randomized Krylov subspace methods that employ the sketch-and-solve paradigm to substantially reduce orthogonalization cost have recently shown great promise in speeding up computations for many core linear algebra tasks (e.g., solving linear systems, eigenvalue problems and matrix equations, as well as approximating the action of matrix functions on vectors) whenever a nonsymmetric matrix is...
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Michael Ackermann (Virginia Tech)5/19/26, 11:25 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
The adaptive Anderson-Antoulas (AAA) algorithm is capable of generating highly accurate rational approximations to given data. Though AAA almost always produces an approximation to a given target accuracy, the degree of the resulting rational function may be larger than actually required to meet the accuracy tolerance. In this talk, we introduce the nonlinear least-squares adaptive...
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Mantas Mikaitis (University of Leeds)5/19/26, 11:25 AMNumerical Linear Algebra in Machine LearningMinisymposium Talk
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput over the software-based matrix multiplication, the multipliers are increasingly used outside of AI, to accelerate various applications in scientific...
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Luka Grubisic (University of Zagreb, Faculty of Science, Department of Mathematics)5/19/26, 11:25 AM
Filtered subspace iterations can be used to approximate a finite cluster of eigenvalues of a lower semi-bounded selfadjoint operator in a Hilbert space. Prototype examples of such operators are Schrödinger operators with short-range potentials. A rational function (filter) of the operator is constructed such that the eigenspace of interest (eigenvalues below the infimum of the essential...
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Bhisham Dev Verma (Wake Forest University)5/19/26, 11:25 AMSparse Tensor Computations: Algorithms and ApplicationsMinisymposium Talk
The Tensor Train (TT) format provides a compact and scalable way to represent high-dimensional tensors, making it essential for solving certain parametrized partial differential equations and other large-scale problems. A critical operation in TT-based computations is rounding, which reduces the ranks of a tensor in TT format to maintain efficiency. While recent randomized rounding algorithms...
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Art J. R. Pelling (Department of Engineering Acoustics, TU Berlin)5/19/26, 11:25 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
While many acoustic systems are well-modelled by linear time-invariant dynamical systems, high-fidelity models often become computationally expensive due the complexity of dynamics. Reduced order modelling techniques, such as the randomized Eigensystem Realization Algorithm (RandERA), can be used to create efficient surrogate models from measurement data. We present an adaptive RandERA...
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Prof. VILMAR TREVISAN (UFRGS - Brazil)5/19/26, 11:25 AM
Within Spectral Graph Theory, Brouwer’s Conjecture (BC) is a fundamental problem concerning Laplacian eigenvalues and graph invariants. It proposes a relationship between the sum of the largest Laplacian eigenvalues of a graph and its number of edges, with direct implications for the study of Laplacian energy. More precisely, for a graph ( G = (V, E) ) with ( n = |V| ) vertices and ( m = |E| )...
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Dr Kirsten Morris (Virginia Tech)5/19/26, 11:25 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Dyadic matrices are a subclass of matrices known as reproducible matrices, where the entries of the matrix are completely determined by their first row. Quasi-dyadic matrices are block matrices with dyadic matrices in the blocks.
There has been extensive work analyzing quasi-cyclic codes, codes defined by quasi-cyclic parity check matrices, but less is known about codes arising from dyadic...
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Shaun Fallat (University of Regina)5/19/26, 11:25 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
An inverse eigenvalue problem for a graph (IEP-G) asks a fundamental question: What are the possible spectra for (symmetric) real matrices fitting a given graph? Many have worked on several aspects of the IEP-G with exciting advances and variations appearing over the past forty years. Here, the focus will be on weighted Laplacian matrices associated with a graph. Such matrices are permanently...
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Christine Andrews-Larson (Florida State University)5/19/26, 11:25 AM
Linear algebra enrollments are increasingly comprised of students from applied STEM majors. Little research has systematically examined the ways in which the curricular resources commonly used in first linear algebra courses relate to the linear algebra applications encountered by students from applied fields in their subsequent coursework and career fields. In this talk, we will summarize...
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DuBose Tuller5/19/26, 11:25 AM
In this talk, I will address using Newton's Method to compute the CP tensor decomposition. The CP optimization problem is a nonlinear least squares problem with factor matrices as the variables. The most common methods for solving CP are Alternating Least Squares (ALS) and Gauss-Newton optimization combined with an iterative method for solving linear systems. I will show that one iteration of...
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Dr Xuzhou Zhan (Beijing Normal University at Zhuhai)5/19/26, 11:25 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
This talk focuses on several stability criteria via Markov parameters for regular matrix polynomials, which generalize the corresponding criteria constrained by the monic assumption. The testing framework employs two finite Hankel matrices, whose rectangular blocks are the submatrices of the Markov parameters redefined through a column-wise splitting and column reduction for matrix...
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361. Singular Value Characterizations for a Nearest Rectangular Polynomial Matrix with an EigenvalueEmre Mengi (Koc University, Istanbul)5/19/26, 11:25 AM
A rectangular polynomial matrix with more columns than rows generically has no eigenvalues. We aim to find a smallest perturbation (with respect to the 2-norm of the concatenated coefficients of the polynomial matrix) so that the perturbed polynomial matrix has an eigenvalue, that is prescribed. This problem is motivated by locating a nearest uncontrollable system for a first-order, as well as...
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Matthias Kleinmann (University of Münster)5/19/26, 11:25 AMConvex Structures in Quantum Information and GravityMinisymposium Talk
Generalized probabilistic theories (GPTs) are a general framework to describe physical theories like quantum mechanics and classical mechanics. At their core, GPTs model prepare-and-measure scenarios by describing preparations and measurements within ordered vector spaces and then predicting measurement outcome probabilities. This framework has been very successful in describing and...
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Nicola Guglielmi (Gran Sasso Science Institute)5/19/26, 11:50 AM
In this talk, I will address eigenvalue-optimization-based matrix nearness problems such as the stability radius of a matrix or a time invariant system, $\mathcal{H}^\infty$ norm computation, the structured distance to singularity.
These are formulated here as 2-variable optimization problems of functionals depending either on a single or on several target eigenvalues of the matrix.
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It is... -
Colby Sherwood (University of Delaware)5/19/26, 11:50 AM
Let $W^i_{k,n}(m)$ denote a matrix with rows and columns indexed
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by the $k$-subsets and $n$-subsets, respectively, of an $m$-element set. The row $S$, column $T$ entry of $W^i_{k,n}(m)$ is 1 if $|S \cap T|= i$, and is 0 otherwise. When $i=k$ the matrix $W^k_{k,n}(m)$ is the subset inclusion matrix for which Wilson found a diagonal form, solving the $p$-rank problem for any prime $p$. This... -
Massimiliano Fasi (University of Leeds)5/19/26, 11:50 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297–313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors $A$ and $B$ are split into integer slices, the product of these slices is computed exactly, and $AB$ is approximated by accumulating these integer products in floating-point...
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Felice Manganiello (Clemson University)5/19/26, 11:50 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a finite field. In this context, we establish an outer bound for the achievable rate region and provide examples of networks where the bound is sharp. We...
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Emmanuel Ameh (Cornell University)5/19/26, 11:50 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Data-driven reduced-order models (ROMs) could enable near-optimal control for very high-dimensional nonlinear dynamical systems, with applications in active flow control such as relaminarizing turbulent flows and recovering from aerodynamic stall. With initial conditions far away from the desired steady state solving the resulting Hamilton-Jacobi-Bellman (HJB) equation, which defines the value...
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Karl Meerbergen (KU Leuven)5/19/26, 11:50 AMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We present an extension of the AAA algorithm, named psvAAA. This MOR method combines the multivariate pAAA and uni-variate set valued AAA method. Many physical systems are described by dynamical systems with physical or geometrical parameters. Often, the system's output is strongly dependent on the Laplace variable or the frequency, and less strong on the parameters. In this talks, we present...
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Guershon Harel (University of California, San Diego)5/19/26, 11:50 AM
As students transition from the mathematics they learn in school years, including their first-year calculus courses, to the first course in linear algebra, they experience discontinuities in their perspective of what mathematics is. Their propensity to continue applying the same habits of learning in the face of this change leads to failure and frustration. The failure manifests itself in the...
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Xingjie Li (UNC Charlotte)5/19/26, 11:50 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
In this presentation, I will begin by introducing shuffled regression and the entropic optimal transport (EOT) as one possible tool for solving shuffled regression. A common approach for this optimization is to use a first-order optimizer, which requires the gradient of the OT distance. For faster convergence, one might also resort to a second-order optimizer, which additionally requires the...
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Dominique Guillot (University of Delaware)5/19/26, 11:50 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We consider general bilinear products parameterized by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower bound in the Loewner order, generalizing previous results...
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Vladimir Druskin (Southern Methodist University)5/19/26, 2:00 PMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
We consider the approximation of $B^T (A+sI)^{-1} B$ for large s.p.d. $A\in\mathbb R^{n\times n}$ with a dense spectrum and $B\in\mathbb R^{n\times p}$, $p\ll n$ using block-Lanczos recursion. We target the computations of MIMO transfer functions for large-scale discretizations of problems with continuous spectral measures, such as linear time-invariant (LTI) PDEs on unbounded domains....
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Prateek Kumar Vishwakarma (Universite Laval, Quebec, Canada)5/19/26, 2:00 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Classical approaches to matrix function theory — i.e., extending scalar functions to matrices — are largely organized around two frameworks: entrywise calculus via the Schur (Hadamard) product, and functional calculus via the spectral theorem. In this talk, I present a third, fundamentally different framework based on matrix convolution, in which convolution itself is viewed as a matrix...
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Alexander Guterman (Bar-Ilan University)5/19/26, 2:00 PM
The first results on transformations preserving matrix invariants is due to Frobenius. This result describes the structure of linear maps $T$ preserving the determinant function, i.e., $\det X = \det T(X)$ for all $X$. Later on there were several extension of this result which are due to Diedonnie, Schur, Dynkin and others.
In 1913 Cullis and then in 1966 independently Radi\'c...
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Allison Fuller (Arizona State University)5/19/26, 2:00 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Block-structured matrices arise as operators in many contexts, including image deblurring and discretized differential equations. These matrices are often large and computationally difficult to work with. By rewriting these operators as a sum of Kronecker products, we may be able to alleviate these challenges. In this talk, we show how we can use the structure of a matrix to impose bounds on...
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Maria Vasilyeva5/19/26, 2:00 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
Nonlinear flow models in heterogeneous porous media lead to large algebraic systems whose efficient solution is often limited by strong nonlinearity and heterogeneity. Fully implicit nonlinear solvers can be computationally expensive, while explicit and/or loosely coupled schemes may suffer from stability issues and slow convergence.
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In this work, we develop a class of linearly implicit... -
Linus Balicki (Novateur Research Solutions)5/19/26, 2:00 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
The parametric adaptive Antoulas–Anderson (p-AAA) algorithm is an effective method for multivariate rational approximation [Carracedo Rodriguez et al., 2023], inspired by the AAA framework for univariate rational approximation [Nakatsukasa et al., 2018].
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In its original formulation, p-AAA aims to approximate a function $\mathbf{f} : \mathbb{C}^d \rightarrow \mathbb{C}$ via a multivariate... -
Zlatko Drmac (Faculty of Science, University of Zagreb)5/19/26, 2:00 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
The Dynamic Mode Decomposition (DMD) is a powerful and versatile numerical method for data driven analysis of nonlinear dynamical systems, with a wide spectrum of applications. It can be used for model order reduction, analysis of latent structures in the dynamics, and e.g. for forecasting and control. The theoretical bedrock upon which the more general Extended DMD (EDMD) framework is built...
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Hayato Arai (University of Tokyo)5/19/26, 2:00 PMConvex Structures in Quantum Information and GravityMinisymposium Talk
In quantum theory, POVMs form the maximal class of measurements compatible with the Born rule. Operational reconstructions motivate a broader convex framework—General Probabilistic Theories (GPTs)—specified by a convex state space and its dual cone of affine measurement functionals.
Within GPTs one can define “non-positive POVMs” (N-POVMs): Hermitian effects summing to the unit but not...
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Xiaobo Liu (Max Planck Institute for Dynamics of Complex Technical Systems)5/19/26, 2:00 PMNumerical Linear Algebra in Machine LearningMinisymposium Talk
Reduced rank extrapolation (RRE) is a classic acceleration method for vector-valued fixed-point process, commonly airsing from iterative solution of algebraic equations. In this talk, we discuss the generalization of this extrapolation framework to sequences of low-rank matrices generated by iterative methods for large-scale matrix equations, such as low-rank alternating directions implicit...
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Charlotte Vermeylen (KU Leuven)5/19/26, 2:00 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
A novel optimization framework is proposed for solving the low-rank tensor approximation problem using the canonical polyadic decomposition (CPD). This can be a difficult optimization problem for certain tensors, e.g., due to degeneracy, i.e., a tensor that can be approximated arbitrarily closely by an ill-conditioned tensor of lower rank. This is one of the phenomena that are encountered in...
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Tahamina Akter (TU Braunschweig)5/19/26, 2:00 PMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
We analyze two parallel numerical strategies for computing selected entries of the matrix inverse of large, sparse, symmetric systems: The selected inverse method and a factorized approximate inverse method. Both techniques are aimed at computations via LU factorizations or incomplete LU (ILU) factorizations. The selected inverse approach exploits the LU/ILU factorization to recover the...
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Kevin Vander Meulen (Redeemer University)5/19/26, 2:00 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
A matrix $A$ has the non-symmetric strong spectral property (nSSP) if $X=O$ is the only matrix which satisfies $A\circ X=O$ and $AX^T=X^TA$. This property comes with implications for eigenvalue properties of sign patterns, including a bifurcation lemma and superpattern lemma. We describe some classes of sign patterns for which every matrix with the sign pattern will have the nSSP. We also...
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Sachin Somra (South Asian University, New Delhi)5/19/26, 2:00 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
In this paper, I study perfect codes and the biclique partition number in graphs, with a special focus on Cayley sum graphs and signed graphs. Perfect codes, which play an important role in coding theory and error correction, were first introduced in graphs by Norman Biggs. Later, Zhou (2016) extended this concept to Cayley graphs and investigated their structural properties. Building on these...
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Etna Lindy (Aalto University)5/19/26, 2:00 PM
In the talk, I will go through our recent work regarding the Smith form of the Sylvester and Bézout resultant matrices. The partial multiplicities associated to the eigenvalue of a polynomial matrix tell us about the conditioning of computing the eigenvalue. Since the eigenvalues of the resultant matrices are the roots of the system, the partial multiplicities are connected to the stability of...
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Steve Mackey (Western Michigan University)5/19/26, 2:25 PM
Over the last two decades, a number of methods for constructing linearizations of matrix polynomials have been developed, including ansatz spaces, Fiedler pencils, and block minimal basis pencils. These methods have also been extended in various ways to apply to matrix polynomials expressed in non-monomial bases. However, these extensions have often been achieved one basis at a time, without...
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David Thorsteinsson (KU Leuven)5/19/26, 2:25 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Block term decomposition (BTD) unifies the two most common tensor decompositions: canonical polyadic and Tucker. While BTDs have found a broad range of applications from machine learning to blind source separation, all known algorithms for computing BTDs were historically optimisation-based, and required the desired block sizes to be specified as input. Recently, algebraic BTD algorithms have...
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Ryo Takakura (University of Osaka)5/19/26, 2:25 PMConvex Structures in Quantum Information and GravityMinisymposium Talk
In quantum theory, certain observables cannot be measured simultaneously, a feature known as measurement incompatibility. This concept captures a fundamental limitation of quantum measurements and has deep connections to quantum phenomena. In this talk, we propose an operational framework to characterize measurement incompatibility using restricted sets of states, modeled as convex subsets. We...
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Elle Buser (Emory University)5/19/26, 2:25 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
Good estimates of hyperparameters can be critical for solving inverse problems accurately, but estimating these hyperparameters often requires solving a challenging and expensive optimization problem involving log determinants. In this work, we consider two optimization approaches, both of which involve stochastic average approximations (SAA) of the objective function. The first approach...
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Athanasios Antoulas (Rice University)5/19/26, 2:25 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
Purpose of this presentation is to discuss novel descriptor realizations of linear multiple-parameter systems and their connection to nonlinear eigenvalue problems. The work is based on recent developments of the Loewner framework as exposed in a SIAM Review paper, published in November 2025.
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Elizabeth Dinkelman (George Mason University)5/19/26, 2:25 PM
The polytope $ASM_n$, the convex hull of the $n\times n$ alternating sign matrices, was introduced by Striker and by Behrend and Knight. A face of $ASM_n$ corresponds to an elementary flow grid defined by Striker, and each elementary flow grid determines a doubly directed graph defined by Brualdi and Dahl. We show that a face of $ASM_n$ is symmetric if and only if its doubly directed graph...
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Nathaniel Pritchard (The University of Oxford)5/19/26, 2:25 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed using SVD-based approaches such as truncated SVD or RandomizedSVD. Although these SVD approaches---especially RandomizedSVD---have proven to be very...
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Jephian C.-H. Lin (National Yang Ming Chiao Tung University)5/19/26, 2:25 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
A sign pattern is a matrix whose entries are in $\{+, -, 0\}$, while its quantitative class is the set of real matrices whose entries match the corresponding signs. A sign pattern is said to be spectrally arbitrary if its quantitative class contains matrices demonstrating all possible monic real polynomials as the characteristic polynomials. Historically, there are the Jacobian method, the...
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Stanislav Budzinskiy (University of Vienna)5/19/26, 2:25 PMNumerical Linear Algebra in Machine LearningMinisymposium Talk
We address the floating-point computation of compositionally-rich functions, concentrating on LLM inference. Based on the rounding error analysis of a composition, we provide an adaptive strategy to select components of the inner function that need to be recomputed more accurately to improve the numerical stability. We explain how this strategy can be applied to different compositions within a...
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Prof. Thomas Wick (Leibniz University Hannover)5/19/26, 2:25 PMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
In this talk, the matrix-free solution of quasi-static phase-field fracture problems is further investigated. More specifically, we consider a quasi-monolithic formulation in which the irreversibility constraint is imposed with a primal-dual active set method. The resulting nonlinear problem is solved with a line-search assisted Newton method. Therein, the arising linear equation systems are...
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Ibrohim Nosirov (Cornell University)5/19/26, 2:25 PMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
Stochastic Lanczos Quadrature (SLQ) is a popular algorithm for approximating the spectral density of a symmetric matrix $A$ using matrix-vector products. We present a variance reduced implementation of SLQ. This implementation has two key ingredients: a faster problem-specific eigensolver and a carefully implemented selective orthogonalization scheme that we use as a deflation criterion. Our...
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Jie Tian (University of Nevada, Reno)5/19/26, 2:25 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The quaternionic numerical range of a matrix is generally nonconvex, in contrast to the classical complex case. Nevertheless, a theorem of So and Thompson in 1996 asserts that the associated \emph{upper bild} in the complex upper half-plane is always convex.
The original proof of So and Thompson relies on a detailed case-by case and computationally involved analysis, including a reduction...
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Valentino Smaldore (Università degli Studi di Padova)5/19/26, 2:25 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Let $\mathcal{C} = \{c_0, c_1, \ldots, c_{q^k}\} \subseteq \mathbb{F}_q^n$ be a $[n,k]_q$-linear code endowed with the Hamming metric. That is, $\mathcal{C}$ is a $k$-subspace of $\mathbb{F}_q^n$. Let $M_{\mathcal{C}}\in\mathbb{R}^{q^k\times q^k}$ be the distance matrix of the code defined as $(M_\mathcal{C})_{i,j} := d_H(c_i, c_j)=|\{i\colon x_i\neq y_i\}|$. We analyze the spectrum of...
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Cankat Tilki (Virginia Tech)5/19/26, 2:25 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We present an in-depth analysis of the Koopman operator using wavelet transform. Based on this analysis, we construct an invariant subspace for the Koopman operator and introduce wavelet-based observables that span this subspace. Moreover, on this subspace, we study the Koopman operator and its eigendecomposition. To approximate its action numerically over this subspace, we combine Extended...
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H Tracy Hall (none)5/19/26, 2:50 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
The Inverse Eigenvalue Problem for a Graph (IEP-G) asks for the possible spectra of a real symmetric matrix knowing only which off-diagonal entries are non-zero, as described by a graph $G$. Three matrix properties, collectively called the “strong properties”, have become prominent in the study of this problem, due in part to their good behavior with respect to edge deletion and contraction...
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Swanand Khare (Department of Mathematics, Indian Institute of Technology Kharagpur)5/19/26, 2:50 PM
The computation of Greatest Common Right Divisors (GCRDs) is a cornerstone problem in control theory, finding applications in identifying controllable and uncontrollable subsystems, computing intersection of behaviors, and calculating the radius of uncontrollability. The methods to compute the Greatest Common Divisors (GCDs) of scalar polynomials has been researched extensively, but the study...
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Rajarshi Bhattacharjee (University of Massachusetts Amherst)5/19/26, 2:50 PMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
We study the problem of approximating the eigenvectors of an n x n symmetric matrix A with bounded entries using random column sampling. We show that for any eigenvalue $\lambda$ of A, one can compute a vector v satisfying $||Av-\lambda v||_2 \leq \epsilon n$ by sampling $\tilde{O}(\frac{1}{\epsilon^4})$ columns of A. For the eigenvector corresponding to the largest-magnitude eigenvalue, this...
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Alberto Bucci (University of Edinburgh)5/19/26, 2:50 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
We present a new technique for efficiently compressing matrix–vector products in the tensor-train (TT) format, avoiding the explicit formation of intermediate tensors arising from standard MPO–MPS multiplication. The proposed method performs the compression in a single pass, leading to significant computational and memory savings.
From a theoretical point of view, the resulting...
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Zequn Zheng (Louisiana State University)5/19/26, 2:50 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
Canonical polyadic tensor decomposition and approximation are fundamental problems in multilinear algebra with broad applications in signal processing, machine learning, and scientific computing. The difficulty of those problems depends on both the rank and order of the tensors. We introduce a new method for middle-rank tensor approximation and prove a new criterion for reshaping higher-order...
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Ramakrishnan Kannan5/19/26, 2:50 PMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
Analyzing large-scale scientific data—such as molecular dynamics simulations of $MoS_2$ recrystallization—poses significant challenges for traditional methods like Nonnegative Matrix Factorization (NMF), particularly on exascale systems. In this talk, we introduce Low-Rank Approximations with Constraints at Exascale (LORACX), a scalable framework that employs distributed, GPU-accelerated NMF...
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Pedro Paredes (Princeton University)5/19/26, 2:50 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
This talk explores the interplay between coding theory and expander graphs. We will discuss key developments in the design of expander-based codes, including recent advancements that lead to locally testable codes and efficient quantum codes. This includes a review of work dedicated to designing vertex expanders and unique-neighbor expanders, focusing on the specific properties that make them...
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Amy de Castro (University of Utah)5/19/26, 2:50 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Constructing low-order approximations to a high-dimensional manifold is a well-studied field as these types of problems arise naturally from the solution of parametric partial differential equations in multi-query or optimization contexts. Full-order approximations, although the most accurate approach to reconstructing a solution manifold, incur too high of an expense in these scenarios....
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James Nagy (Emory University)5/19/26, 2:50 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
In recent years a substantial amount of work has been done on developing mixed-precision algorithms for linear systems, methods that can exploit capabilities of modern GPU architectures. However, very little work has been done for ill-conditioned problems that arise from large-scale inverse problems. Special considerations, which normally do not arise when solving well-conditioned problems,...
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Meiling Deng (University of Nevada, Reno)5/19/26, 2:50 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this talk, we investigate the eigenvalue problem for third-order quaternionic tensors. We first introduce the notion of right T-eigenvalues and develop an efficient algorithm for their computation, whose effectiveness is demonstrated through comparative numerical experiments.
For Hermitian quaternionic tensors, we then derive bounds for the eigenvalues of tensor sums and extend Weyl’s...
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Sean Reiter (Courant Institute of Mathematical Sciences, New York University)5/19/26, 2:50 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
In recent years, structured reduced-order modeling has become an essential component in meaningful applications across engineering and the physical sciences whenever mathematical models are unavailable, but input-output data are abundant. For linear time-invariant systems, the Loewner framework provides a non-intrusive methodology for the construction of minimal interpolants from rational...
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Lucas Siviero Sibemberg (UFRGS)5/19/26, 3:45 PM
The underlying graph $G$ of a symmetric matrix $M=(m_{ij})\in \mathbb{R}^{n\times n}$ is the graph with vertex set $\{v_1,\ldots,v_n\}$ such that a pair $\{v_i,v_j\}$ with $i\neq j$ is an edge if and only if $m_{ij}\neq 0$. For a graph $G$, let $q(G)$ denote the minimum number of distinct eigenvalues among all symmetric matrices whose underlying graph is $G$. A symmetric matrix $M$ is a...
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Julio Moro (Universidad Carlos III de Madrid)5/19/26, 3:45 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
The Real Nonnegative Inverse Eigenvalue problem (hereforth, RNIEP) consists, for a given positive integer n, in characterizing the lists of n real numbers which are the spectrum of some n × n matrix with real entries. C-realizability was originally introduced in [1] as a sufficient condition for the RNIEP. It was shown back then that C-realizability included as particular cases most of the...
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Lauri Nyman (University of Manchester)5/19/26, 3:45 PM
In this talk, we consider the theoretical convergence of flexible GMRES. While convergence of standard GMRES is well studied, there exist few results of similar nature for flexible GMRES. The aim of this talk is to discuss and fill in this gap. In addition, we report on experiences of using these ideas in the context of randomized sketching.
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John Byrne (University of Delaware)5/19/26, 3:45 PM
Let $F$ be a digraph. What is the largest possible minimum outdegree on an $n$-vertex digraph which does not contain a copy of $F$? I will discuss algebraic approaches to this question and present some of my related work (joint with Michael Tait).
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Esther Gallmeier (Cornell University)5/19/26, 3:45 PMTheoretical Advances in Operator LearningMinisymposium Talk
The goal underlying our work is to develop provably accurate and data-efficient learning algorithms for non-self-adjoint operators using only input-output pairs. State-of-the-art approximation techniques with fast convergence rates either apply only to self-adjoint operators or require access to the adjoint operator, which is unavailable in experimental settings and often difficult to access...
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Mr Deven Mhadgut (Graduate Student, Aerospace and Ocean Engineering Department)5/19/26, 3:45 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
Bistable tape spring booms are used in space structures for their ability to self-deploy using stored strain energy. However, their uncontrolled deployment can induce mechanical shocks that may damage sensitive satellite components. In the past, researchers have focused on mitigating these shocks through damping materials and active control techniques. Accurate prediction of deployment-induced...
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Ioana Dumitriu (University of California, San Diego)5/19/26, 3:45 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
The fastest method for diagonalizing a nonsymmetric matrix or matrix pencil is pseudospectral divide-and-conquer. This two-step algorithm diagonalizes a matrix/pencil by (1) randomly perturbing the input(s) and (2) running fast (and highly-parallel) spectral divide-and-conquer. The key to this approach is the random perturbation, which with high probability implies a guarantee of...
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Md Taufique Hussain (Wake Forest University)5/19/26, 3:45 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy compared to traditional matrix methods. Under the $\star_M$ tensor framework, tensors can be decomposed in a matrix-mimetic way, including using the $\star_M$...
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Ron Morgan (Baylor University)5/19/26, 3:45 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
The BiCG method for solving linear equations has a polynomial at its core. The new Twin BiCG method solves multiple right-hand systems using the same polynomial for each system. This polynomial is applied implicitly by using the parameters from solving the first right-hand side for all of the systems. Twin BiCG has automatic stability control from the extra copies of eigenvalues that are...
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Haibo Li (Huazhong University of Science and Technology)5/19/26, 3:45 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In this talk, I will present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method for solving ill-posed linear inverse problems. This method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive reproducing kernel Hilbert space (RKHS) penalizing the spaces of small singular values. At the core of the method is a new generalized...
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Ms Mamta Verma (Dr B R Ambedkar National Institute of Technology Jalandhar, 144008, Punjab, India)5/19/26, 3:45 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this work, we study some inequalities for positive linear maps in the context of spectral graph theory. In particular, we present both existing and new bounds for the spread of matrices associated with graphs, expressed in terms of graph invariants.
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Bryan Shader (University of Wyoming)5/19/26, 3:45 PM
This talk discusses problem of determining the minumum number of nonzero entries in a pair of matrices (A,A^(-1)) for A in various families of matrices (e.g. irreducible, fully indecomposable, primitive, positive definite, orthogonal, symmetric with connected graph, irreducible covariance matrices). Some of the results are from work with H. Gupta, L. Hogben and T. Wong.
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Feliks Nueske (Max-Planck-Institute DCTS Magdeburg)5/19/26, 3:45 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
In this talk, I will present recent work on analysing time series data for complex dynamics. Extended dynamic mode decomposition (EDMD, Williams et al, 2015) is a widely used algorithm to learn a linear surrogate model for the statistics of an evolving dynamics, based on the Koopman operator framework. For high-dimensional systems, choosing a suitable basis set can become challenging, as...
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Robert van de Geijn (The University of Texas at Austin)5/19/26, 3:45 PM
The National Research Council in a 2000 report defined mathematical proficiency as a combination of Understanding, Computing, Applying, Reasoning, and Engaging (UCARE). We share how this guided course content development as we determined the knowledge and skills requirements for our undergraduate and graduate linear algebra courses. Building mathematical proficiency in linear algebra goes...
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Geir Dahl5/19/26, 4:10 PM
We introduce a new rank concept for $(0,\pm 1)$-matrices, called the $\pm$-rank of a $(0,\pm 1)$-matrix. This ``generalizes'' the binary rank and the term rank of (0,1)-matrices. We establish several inequalities relating the different ranks, including ordinary real rank. Moreover, the $\pm$-rank is discussed for certain classes of $(0,\pm 1)$-matrices, such as alternating sign matrices...
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Helena Šmigoc (University College Dublin)5/19/26, 4:10 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
The nonnegative inverse eigenvalue problem (NIEP) seeks to characterize the multisets of complex numbers that can be realized as the spectra of nonnegative matrices. Hessenberg matrices have been used in several central constructive results within this field, including the resolution of the NIEP for $4 \times 4$ matrices, the characterization of spectra where all non-Perron eigenvalues possess...
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Divya Taneja (Indian Institute of Technology Kharagpur)5/19/26, 4:10 PM
The distance matrix of a graph G, denoted by D(G), is an n x n matrix with its rows and columns indexed by a set of vertices, V(G). For i ̸= j, the (i, j)-entry, dij, of D(G) is a set equal to d(i, j). Also, dii = 0, i = 1, ..., n. Here, d(i, j) denotes the distance between the vertices i and j, which is the length of a shortest i−j path. The distance spectrum of a graph is the set of...
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Ryan Schneider (University of California Berkeley)5/19/26, 4:10 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
While pseudospectral divide-and-conquer is optimal for nonsymmetric eigenvalue problems (in terms of both arithmetic and communication complexity) it is not currently implemented in any of our standard numerical linear algebra libraries. This is due to both the difficulty of translating the algorithm's technical pseudocode into something practical and to the challenge of preparing users for a...
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Geshuo Wang (University of Washington)5/19/26, 4:10 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT) format. The key idea is to discretize the three-dimensional velocity variable using tensor trains while treating the spatial variable as a parameter,...
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Dr Asuman Oktaç (Cinvestav)5/19/26, 4:10 PM
In the first part of the talk, I will briefly explain the APOS (Action—Process—Object—Schema) theory and how it is applied to the teaching of mathematical concepts as well as to research on learning. In this approach, the mental construction of a mathematical concept is modeled by means of structures that give the theory its name, and mental mechanisms that allow the passage to new structures....
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Kyle Monette (University of Rhode Island)5/19/26, 4:10 PM
Given a symmetric tridiagonal matrix, it has been well--established, that in exact arithmetic, applying some of its eigenvalues as shifts via the $QR$ strategy produces a particular structured matrix where the leading tridiagonal block contains the non--shifted eigenvalues and a trailing diagonal submatrix of the shifted eigenvalues. We will show that the leading tridiagonal block can be...
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Daniele Toni (Scuola Normale Superiore)5/19/26, 4:10 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
We present randomized algorithms for estimating the log-determinant of regularized symmetric positive semi-definite matrices. The algorithms access the matrix only through matrix vector products, and are based on the introduction of a preconditioner and stochastic trace estimator.
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We claim that preconditioning as much as we can and making a rough estimate of the residual part with a small... -
David Persson (New York University & Flatiron Institute)5/19/26, 4:10 PMTheoretical Advances in Operator LearningMinisymposium Talk
We present a randomized algorithm for producing a quasi-optimal hierarchically semi-separable (HSS) approximation to an $N\times N$ matrix $A$ using only matrix-vector products with $A$ and $A^T$. We prove that, using $O(k \log(N/k))$ matrix-vector products and $O(N k^2 \log(N/k))$ additional runtime, the algorithm returns an HSS matrix $B$ with rank-$k$ blocks whose expected Frobenius norm...
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Luka Marohnić (Zagreb University of Applied Sciences)5/19/26, 4:10 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We introduce an AAA-type method for rational quasi-Hermite approximation formulated in barycentric form. A stacked Hermite–Löwner matrix is assembled from function values and derivative data at adaptively selected support nodes, and the barycentric weights are determined through a homogeneous least-squares procedure. This approach eliminates the need for external test points as required in the...
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Fengjiao Liu (FAMU-FSU College of Engineering)5/19/26, 4:10 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this talk, we first investigate the maximal interval of existence for the solution of a symmetric matrix Riccati differential equation. Then, we apply this result to study the reachability of the closed-loop state transition matrix for a linear time-varying system over a finite time interval. Under a mild assumption, we characterize the set of closed-loop terminal state transition matrices...
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Jonas Bresch (Technische Universität Berlin)5/19/26, 4:10 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra.
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Conventional algorithms for its computation typically rely on matrix-adjoint products,
making them sensitive to errors arising from adjoint mismatches.
To address this issue, we introduce a stochastic zeroth-order Riemannian algorithm
that maximizes the generalized Rayleigh... -
Fan Tian5/19/26, 4:10 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
Tensor decomposition is widely used for analyzing multi-way data in various applications that often involve continuously generated data. Efficient methods to process and extract meaningful patterns dynamically are hence essential for these applications. In this talk, we consider the problem of computing the streaming tensor BM-decompositions (BMD). An incremental algorithm, OnlineBMD, is...
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Igor Balla (Leipzig University)5/19/26, 4:10 PM
In this talk, we will present a proof of the fact that Boolean matrices with bounded $\gamma_2$-norm or bounded normalized trace norm must contain a linear-sized all-ones or all-zeros submatrix, verifying a conjecture of Hambardzumyan, Hatami, and Hatami. We will also discuss further structural results about Boolean matrices of bounded $\gamma_2$-norm and applications in communication...
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Shengtong Zhang (Stanford University)5/19/26, 4:35 PM
Cosine polynomials of the form $$f(x) = \cos(a_1 x) + \cos(a_2 x) + … + \cos(a_n x)$$ appear extensively in number theory and combinatorics. An old problem of Ankeny and Chowla asks: if $a_1, \cdots, a_n$ are distinct positive integers, how small must the minimum value of $f(x)$ on $[0, 2\pi]$ be? Concurrently with Benjamin Bedert, we show that the minimum value of $f(x)$ must be polynomial in...
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Antti Hannukainen (Aalto University)5/19/26, 4:35 PM
I discuss solving large-scale symmetric and positive definite eigenproblems in distributed computing environments where communication between tasks is expensive, such as a cluster of networked workstations running the HTCondor batch system. As a model problem, I consider computing a few smallest eigenvalues of several eigenproblems related to FE-discretization of elliptic PDEs. The matrices...
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Sima Ahsani (Washington and Lee University)5/19/26, 4:35 PM
This talk will discuss the integration of undergraduate research and project-based learning in both abstract and computational linear algebra. Specifically, it will highlight a research training course focused on the mathematical foundations of machine learning and the analysis of human brain connectivity.
Throughout a summer research program and a Python-based numerical linear algebra...
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Wasin So (San Jose State University)5/19/26, 4:35 PM
The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of all the eigenvalues of its adjacency matrix. Gutman (2001) proposed a problem of characterizing the graph $G$ and the edge $e$ of $G$ such that $\mathcal{E}(G-e) \le \mathcal{E}(G)$. Later, Day and So (2008) gave a sufficient condition : $e$ is a cut-edge of $G$.Recently, Tang et al. (2023) gave another...
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George Stepaniants (California Institute of Technology)5/19/26, 4:35 PMTheoretical Advances in Operator LearningMinisymposium Talk
The simulation of multiscale viscoelastic materials poses a significant challenge in computational materials science, requiring expensive numerical solvers that can resolve dynamics of material deformations at the microscopic scale. The theory of homogenization offers an alternative approach to modeling, by locally averaging the strains and stresses of multiscale materials. This procedure...
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Miriam Pisonero (Universidad de Valladolid, Spain)5/19/26, 4:35 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterizing the lists $\sigma$ of $n$ complex numbers (counting multiplicities) that are the spectrum of a nonnegative matrix of size $n$. A list $\sigma$ is said to be realizable if there exists a nonnegative matrix whose spectrum is $\sigma$.
Another way of facing the NIEP is to focus the attention on the...
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Amit Subrahmanya (Argonne National Laboratory)5/19/26, 4:35 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We address optimal sensor placement for Bayesian nonlinear inverse problems by formulating the task as a matrix column subset selection problem. The design matrix is derived from the expected information gain criterion. Although the resulting solutions are not necessarily globally optimal, the approach presents a rapid time to solution. The effectiveness of the method is demonstrated on...
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Diana Halikias (New York University)5/19/26, 4:35 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operator while only using data generated by the forward action of the operator without access to the adjoint. However, naively, it seems essential to sample the action of the adjoint....
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Vishwas Rao5/19/26, 4:35 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We propose using the starM tensor product framework for constructing Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM) reduced order models. By exploiting the inherent multidimensional relationship structure of snapshot data, the approach enables efficient computation of the reduced bases. Operating directly on tensor representations reduces storage and...
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Joshua Cooper (University of South Carolina)5/19/26, 4:35 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Pressing sequences of simple undirected graphs totally colored by a field arise naturally in computational phylogenetics, where (over $GF(2)$) they are in bijection with sortings-by-reversal of signed permutations which model gene sequences in related organisms. They can be viewed in several surprising different ways, including as any consecutive initial sequence of rows whose diagonal...
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Jesse Geneson (San José State University)5/19/26, 4:35 PM
A 0–1 matrix is P-saturating if it avoids a fixed forbidden pattern P but contains P after changing any zero entry to one. The associated saturation function asks for the minimum number of ones in such a matrix. In this talk I will describe a structural theory of saturation for 0–1 matrices, centered on a sharp dichotomy: for every fixed pattern P, the saturation function is either bounded or...
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Boris Kramer (University of California San Diego)5/19/26, 4:35 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) arise in various settings in optimal control and model order reduction, and their solutions are notoriously difficult to acquire. For linear time-invariant systems, the HJB PDEs of interest typically simplify to matrix algebraic equations, such as the algebraic Riccati equation or the matrix Lyapunov equation, for which many...
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Fabio Matti (EPFL)5/19/26, 4:35 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Stochastic trace estimators are a family of widely used techniques for approximating traces of large matrices accessible only via matrix-vector products. These methods have been studied extensively when applied to constant matrices $B$. We analyze three standard stochastic trace estimators—the Girard-Hutchinson, Nyström, and Nyström++ estimators—when they are applied to parameter-dependent...
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Leonie Van Pottelberghe (KU Leuven)5/19/26, 4:35 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
Recent contributions for rational approximation include the p-AAA method (and variations) and the extension of the Loewner framework to multiple dimensions. These contributions are recent and are inspiration for further analysis and algorithmic improvements.
In this talk, we combine two ingredients that have proven to be successful in their respective contexts, i.e., the AAA method for...
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Emanuel Juliano (Federal University of Minas Gerais)5/19/26, 5:00 PM
In the 1980s, using the software Graffiti, Fajtlowicz made a conjecture relating the independence number of a graph with its energy, a spectral parameter introduced by Gutman (1978). By formulating the graph energy as a semidefinite program (SDP), we take a step towards Fajtlowicz's conjecture, relating the graph energy to the fractional clique covering number. As a byproduct of the SDP...
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Aryeh Keating (Virginia Tech)5/19/26, 5:00 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and structural constraints. However, classical regularization formulations are frequently infeasible in this setting due to prohibitive memory requirements,...
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Christopher Beattie (Virginia Tech)5/19/26, 5:00 PMTheoretical Advances in Operator LearningMinisymposium Talk
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption has lagged behind traditional, covariance-based approaches, in part because the intrinsic formulation has lacked an accompanying toolkit of computational...
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Richard A Brualdi (University of Wisconsin-Madison)5/19/26, 5:00 PM
A permutation $i_1i_2\cdots i_n$ is Gilbreath provided it does not contain a consecutive pattern 132 or 312. The corresponding $n\times n$ permutation matrices are the Gilbreath permutation matrices*. Gilbreath permutations arise from classical riffle shuffling of a deck of cards. The number of Gilbert permutations is $2^{n-1}$. Gilbreath permutation matrices are seen to be unimodal. An...
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Akil Narayan (University of Utah)5/19/26, 5:00 PMRational Approximation and Interpolation: Practical Applications, Challenges and SolutionsMinisymposium Talk
We discuss analytical estimates for greedy construction of rational approximations, where the underlying function is the linear sketch of an operator resolvent. The canonical example of this setup is the transfer function of a linear dynamical system. Under a sectorial assumption for the operator, this analysis immediately reveals corresponding algorithms, and provides explicit estimates of...
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Paul Zachlin (Lakeland Community College)5/19/26, 5:00 PM
We study eigenvalue inclusion regions first defined by Householder and explore applications to large, sparse matrices. We also study pseudospectra and relative pseudospectra, which are similarly defined eigenvalue inclusion regions. Then we explore connections between these sets.
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Zhen Huang5/19/26, 5:00 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Recent advances in the simulation of non-Markovian open quantum systems have motivated renewed interest in Krylov-based methods for computing steady states. In this talk, we explore optimal strategies and theoretical insights underlying these approaches, and present efficient algorithms developed in both the MArVEL framework and tensor network representations. Together, these methods offer a...
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Peter Benner5/19/26, 5:00 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Learning compact surrogate models from data has become a major application area of machine learning techniques. Such models are required to describe dynamical behavior of processes in the presence of time series data and the absence of explicit mechanistic models. This may be the case if only measurement data is available or simulation data is obtained via proprietary software. Prominent...
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Jitul Talukdar (IIT Kharagpur)5/19/26, 5:00 PM
Abstract: In this paper, we investigate when the disjoint union of complete graphs $K_a \cup K_b$ is determined by its signless Laplacian spectrum (Q-DS). We first prove that $K_a \cup K_b$ is Q-DS among disconnected graphs. We then show that no connected signless Laplacian co-spectral mate of $K_a \cup K_b$ exists on at most ten vertices. Further, we establish that $K_t \cup K_a$ is Q-DS for...
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Raphael Loewy (Technion-Israel Institute of Technology)5/19/26, 5:00 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
We consider polynomials preserving nonnegative matrices. Let $n, m$ be positive integers, and
$P_{n}=\{p \in R[x]: p(A)\geq 0 \mbox{ for all } A \geq 0, A \in {R}^{n,n}\}$, $P_{n,m}=\{p \in P_{n} : deg(p) \leq m \}$.
$P_{n}$ was defined by Loewy and London, motivated by the Nonnegative Inverse Eigenvalue Problem but is of independent interest. Given any polynomial $p$, identify $p$ with...
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Heather Wilber (University of Washington)5/19/26, 5:00 PMNew Directions and Challenges in Linear AlgebraMinisymposium Talk
In low rank approximations to kernel matrices, skeletons consist of subsets of rows and columns from which CUR, ID, and related approximations can be formed. We consider applications in which parameter-dependent families of matrices with numerical low rank structures appear, such as in parameter dependent partial differential equations. We develop new techniques for analyzing and constructing...
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Prof. Joe Kileel (University of Texas, Austin)5/19/26, 5:00 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
In this talk, I will present a new method for maintaining low-rank CP decompositions of tensorial data streams. Numerical results indicate that the approach has acceptable computational costs at scale, while significantly improving accuracy and adaptivity to changes in the data stream compared to existing methods. Convergence theory will be provided, in addition to demonstrations on real...
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Matthew Mauntel (Tarleton State University)5/19/26, 5:00 PM
In this talk, we will discuss a game within the video game Vector Unknown:Echelon Seas (VUES) that focuses on matrix multiplication. VUES was designed by a group of students at Arizona State University in collaboration with mathematics educators and computer scientists. The 3D video game allows students to select one of four matrices (represented by cannonballs) and one of four vectors...
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5/20/26, 8:20 AM
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Haim Avron (Tel Aviv University)5/20/26, 8:30 AM
The field of quantum computing offers a unique opportunity to revolutionize numerical linear algebra and scientific computing. This stems from the ability of quantum computers to efficiently model complex structures, and to represent and manipulate high-dimensional vectors and matrices using exponentially fewer qubits. These advantages arise from the fundamental principles of superposition and...
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Aida Abiad (Eindhoven University of Techonolgy)5/20/26, 9:25 AM
One of the main goals in spectral graph theory is to deduce the principal properties and structure of a graph from its graph spectrum. In this talk we will show how spectral graph theory provides powerful methods for obtaining results concerning substructures of graphs, and also how these results can be useful in other mathematical fields such as coding theory. In particular, we will derive...
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Avi Berman (Technion)5/20/26, 11:00 AM
Laffey and Smigos proved that every 2x2 integer nonnegative PSD matrix can be decomposed as BB^t, where B is integer nonnegative and the number of columns of B is not more than 11. We show that 11 can be reduced to 10 ans suggest as an open problem the conjecture that it can be reduced to 9.
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Kévin Carrier (École Polytechnique (France))5/20/26, 11:00 AM
The security of code-based cryptography relies fundamentally on the computational hardness of decoding random linear codes. Until recently, the most efficient known algorithms for the decoding problem were Information Set Decoding (ISD) algorithms, which we refer to as primal attacks in this presentation.
In 2001, a new class of decoding algorithms, known as dual attacks, was introduced and...
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Jamie Sikora (Virginia Tech)5/20/26, 11:00 AMConvex Structures in Quantum Information and GravityMinisymposium Talk
Identifying quantum states is one of the oldest problems in quantum information theory. In this work, we explore a variation of this task: rather than determining which state a system is in, we seek to identify a state that it is not. A set of quantum states is said to be antidistinguishable if this inverse guessing game can be won with certainty. We establish tight bounds characterizing when...
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Asma Farooq (Gran Sasso Science Institute, L'Aquila, Italy)5/20/26, 11:00 AM
Nonlinearity often leads to slow or unstable convergence in iterative solvers for nonlinear least-squares problems. In this work, we introduce a family of accelerated algorithms that leverage a periodically restarted variant of the Generalized Minimum Residual (GMRES) method to address these challenges. The use of restarting strategies not only mitigates computational overhead but also...
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Carolyn Reinhart (Swarthmore College)5/20/26, 11:00 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
Zero forcing is a graph coloring process in which a set of initially blue vertices force the remaining vertices in the graph to be colored blue after repeated applications of a color change rule. Leaky forcing is a fault-tolerant variant of zero forcing in which some set of $\ell$ vertices, called leaks, are forbidden from forcing. The $\ell$-leaky forcing number is the size of the smallest...
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Mr Alexander Zadorojnov (Faculty of Computer and Information Science, Ben-Gurion University of the Negev)5/20/26, 11:00 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
With the growing global demand for energy, natural gas is playing an increasingly important role in modern energy systems. Gas transmission networks, which deliver the gas, also offer a unique opportunity for large-scale energy storage through the pipelines themselves. However, efficient utilization of the networks requires careful operation subject to pressure constraints, operational costs,...
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Marc Aurèle Gilles (Princeton University)5/20/26, 11:00 AMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
I will present Randomly Pivoted LU (RPLU), a randomized variant of Gaussian elimination with complete pivoting that samples pivots proportional to squared Schur-complement entries, and analyze its low-rank approximation properties. I will highlight two regimes where RPLU is particularly effective at low-rank approximation: (i) memory-limited settings, where a rank-$k$ approximation can be...
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Amit Upadhyay (Indian Institute Of Technology (Indian School Of Mines) Dhanbad)5/20/26, 11:00 AMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
Preconditioned BiCGStab is a widely used Krylov subspace method for solving large sparse nonsymmetric linear systems. Motivated by modern computing architectures, recent implementations increasingly adopt mixed-precision arithmetic, most commonly applying the preconditioner in low precision while performing all other operations in high precision. Recent work by Anciaux-Sedrakian et al. (2024)...
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Alejandro Diaz (Sandia National Laboratories)5/20/26, 11:00 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
This talk presents an interpretable, non-intrusive reduced-order modeling technique for parameterized problems using regularized kernel interpolation. Parameterized reduced-order models (ROMs) enable the rapid approximation of PDE solutions corresponding to a given parameter, thus accelerating uncertainty quantification or inverse problem workflows requiring many PDE solves. Existing...
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Prof. Ning Zheng (Tongji University)5/20/26, 11:00 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
For solving noisy linear ill--posed problems arising from the practical applications, the residual based iterative methods may suffer semi-convergence phenomenon, where the iterates initially get closer to the desired solution but then degrade as the iteration continues. Building upon the randomized Gram--Schmidt algorithm, a random sketching technique known to reduce inner product...
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Sudipta Mallik (Marshall University)5/20/26, 11:00 AM
Given an integer k, deciding whether a graph has a clique of size k is an NP-complete problem. Wilf's inequality provides a spectral lower bound for the clique number (i.e., the order of a largest clique) in terms of the largest adjacency eigenvalue. In 2018, Elphick and Wocjan conjectured a stronger spectral bound using positive adjacency eigenvalues. We introduce a spectral bound using...
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Dr Rick Archibald (Oak Ridge National Laboratory)5/20/26, 11:00 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
The exponential growth of scientific data from simulations and experiments demands efficient compression techniques for storage and processing. This talk introduces a novel streaming weak-SINDy algorithm designed for real-time compression of streaming scientific data. Leveraging the underlying structure of physical systems, the algorithm constructs memory-efficient feature matrices and target...
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Gil Goldshlager (UC Berkeley)5/20/26, 11:00 AMTheoretical Advances in Operator LearningMinisymposium Talk
An increasing number of theoretical results are available to characterize the extent to which neural networks can (i) represent scientifically relevant functions and operators, and (ii) learn these functions and operators from data. However, even with the right network architecture and the right dataset, optimization is a bottleneck. On the one hand, popular machine learning optimizers such as...
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Günhan Caglayan (New Jersey City University, Mathematics Department)5/20/26, 11:00 AM
Symmetric (real) and Hermitian (complex) matrices occupy a central role in linear algebra due to their well-known spectral properties, including real eigenvalues and mutually orthogonal eigenvectors. While these results are theoretically elegant, students often struggle to develop geometric intuition for eigenvalues, eigenvectors, and matrix transformations, especially in higher...
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Anna Davis (The Ohio State University), Paul Zachlin (Lakeland Community College)5/20/26, 11:25 AM
In January 2023, the authors published the second edition of Linear Algebra: An Interactive Introduction, which the speaker shared at the ILAS Education Session at JMM in Boston.
Thanks to a $ 2.1 million grant from the United States Department of Education entitled “Fortifying Open Education: Scaling Ximera for Enduring Impact”, the authors have been able to enhance the online textbook in...
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Xiaozhe Hu (Tufts University)5/20/26, 11:25 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
Multigrid (MG) methods are efficient and scalable for solving sparse linear systems arising from the discretization of partial differential equations (PDEs). However, the performance of standard V- and W-cycle MG methods often deteriorates as the physical and geometric complexity of the PDEs increases. To remedy this, the Algebraic Multilevel Iteration (AMLI)-cycle was developed, utilizing...
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Pawan Kumar (International Institute of Information Technology, Hyderabad)5/20/26, 11:25 AMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
As Large Language Models (LLMs) scale toward the trillion-parameter mark, the industry is hitting a "memory wall." Traditional compression-like simple pruning or standard SVD-often forces a trade-off between model quality and hardware efficiency. In this talk, we dive into Hierarchical Sparse Plus Low-Rank (HSS) compression, a novel framework that achieves state-of-the-art bit-per-parameter...
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Matthias Voigt (UniDistance Suisse)5/20/26, 11:25 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Kernel methods approximate nonlinear maps in a data-driven way by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel Hilbert space (RKHS), determined solely by the chosen kernel and the dataset, whose elements identify the basis elements. Consequently, the projection operator...
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Enide Andrade (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Portugal)5/20/26, 11:25 AM
Let $G$ be a mixed graph and let $(H_1, H_2)$ be an ordered pair of mixed graphs whose orders coincide with the order and size of $G$, respectively. We introduce the subdivision mixed graph $S(G)$ and the $(H_1,H_2)$-merged subdivision mixed graph. We investigate the Hermitian spectrum and the Hermitian energy of these graphs, deriving spectral properties that relate merged subdivision mixed...
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Prof. Leo Rebholz (Clemson University)5/20/26, 11:25 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We extend a low rank tensor ROM recently developed by Olshanskii et al by enhancing it with continuous data assimilation (CDA). We show how CDA is easily incorporated into the ROM, and analytically show that it provides for theoretical long time error estimates. Numerical tests illustrate the theory and show it is an effective tool for simulating incompressible flow over a wide range of...
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Gereon Koßmann (RWTH Aachen University)5/20/26, 11:25 AMConvex Structures in Quantum Information and GravityMinisymposium Talk
We develop quantitative de Finetti representation theorems beyond standard quantum settings, driven by the principle that permutation symmetry enforces approximate independence at finite extension level. First, using a GPT-motivated notion of relative entropy (via an integral representation) we define mutual information for general convex state spaces and prove a uniform monogamy bound for...
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Lucas Onisk (Emory University)5/20/26, 11:25 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Many problems in science and engineering give rise to linear systems of equations that are commonly referred to as large-scale linear discrete ill-posed problems. The matrices that define these problems are typically severely ill-conditioned and may be rank deficient. Because of this, regularization is often needed to stem the effect of perturbations caused by error in the available data. In...
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Eugenio Turchet (GSSI)5/20/26, 11:25 AM
The nearest correlation matrix problem consists in finding the closest valid correlation matrix to a given symmetric matrix that may fail to be positive semi-definite. In other words, given a symmetric unit-diagonal matrix that is not a proper correlation matrix, one seeks the nearest positive semi-definite matrix with unit diagonal entries.
We address the problem of finding the nearest...
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Naomi Shaked-Monderer (Technion, Israel Institue of Technology and The Max Stern Yezreel Valley College)5/20/26, 11:25 AM
A positive semidefinite matrix $A$, real symmetric or complex ermitian, is said to have factor width at most $k$ if $A=VV^*$, where each column of $V$ has at most $k$ nonzero entries. We call such a factorization a width-$k$ factorization. The factor width of $A$ is the minimum $k$ for which it has a width-$k$ factorization.
In a recent paper [Linear Algebra Appl. 716 (2025) 32–59]...
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Aras Bacho (California Institute of Technology)5/20/26, 11:25 AMTheoretical Advances in Operator LearningMinisymposium Talk
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing their complexity often fails to substantially improve their accuracy, leaving them on par with much simpler approaches such as kernel methods and more traditional reduced-order models. In this article, we set out to...
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Bonnie Jacob (Rochester Institute of Technology)5/20/26, 11:25 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
In this talk, we introduce a new parameter, the orientable forcing number of an undirected graph $G$, which is the maximum zero forcing number among all oriented graphs that have $G$ as their underlying undirected graph. We establish some properties of the orientable forcing number, including extreme values, and discuss how the parameter relates to matrices.
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Veronika Kuchta (Florida Atlantic University)5/20/26, 11:25 AM
We construct a novel code-based blind signature scheme, using the Matrix Equivalence Digital Signature (MEDS) group action. The scheme is built using similar ideas to the Schnorr blind signature scheme and CSI-Otter, but uses additional public key and commitment information to overcome the difficulties that the MEDS group action faces: lack of module structure (present in Schnorr), lack of a...
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Mikhail Lepilov (Rensselaer Polytechnic Institute)5/20/26, 11:25 AMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
Due to the size of many kernel matrices that arise in applications, it is often necessary to work with their low-rank approximations in order to efficiently perform many computations. Low-rank matrix decompositions to such matrices may be quickly obtained by exploiting the analytic structure of the underlying kernel, for example by using Taylor expansions or an integral representation; such...
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Raymond Tuminaro (Sandia National Laboratories)5/20/26, 11:50 AMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
An algebraic multigrid (AMG) algorithm is proposed for curl-curl electro-magnetics PDEs that are discretized with 1st order edge elements. The key idea behind the algorithm centers on generating edge interpolation operators such that certain near null space properties of the discrete curl-curl operator are preserved on coarse levels so that good AMG convergence rates can be obtained....
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Prof. Sepideh Stewart (University of Oklahoma)5/20/26, 11:50 AM
This talk describes the design and features of a newly developed undergraduate course in numerical linear algebra and an accompanying instructor-led research study that examines how students engage with theoretical structure and computational behavior in AI-supported environments.
This course offered an introduction to numerical linear algebra, focusing on its theoretical foundations,...
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Julius Alexander Zeiss (RWTH Aachen)5/20/26, 11:50 AMConvex Structures in Quantum Information and GravityMinisymposium Talk
We apply information-theoretic de Finetti principles to build convergent approximation schemes with explicit finite-level guarantees, yielding both outer relaxations and certified inner points. For polynomial optimization over convex bodies with local equality and inequality constraints, an information-theoretic monogamy argument yields a convergent conic hierarchy whose approximation error...
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Prof. Omar Ghattas (University of Texas, Austin)5/20/26, 11:50 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We introduce Tucker tensor train Taylor series (T4S) surrogate models for high dimensional mappings that depend implicitly on the solution of a partial differential equation. Traditionally, Taylor series are intractable here because the derivative tensors are enormous, and are only accessible through multilinear actions. We overcome these challenges by approximating each derivative tensor with...
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Eshwar Srinivasan (Research Scholar)5/20/26, 11:50 AM
In this paper, we introduce a new matrix property called the I-circular property, which is closely related to the well-known D-circular property introduced by Safe. The I-circular property requires that both the rows of a matrix and the pairwise intersections of rows form circular intervals under some linear ordering of the columns. Our main result is a complete forbidden submatrix...
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Mr Rahmi El Mechri (Univeristà Politecnica delle Marche, Scuola IMT Alti Studi Lucca)5/20/26, 11:50 AM
Given two linear codes, the Permutation Equivalence Problem (PEP) asks to find a permutation that maps one code onto the other.
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The state-of-the-art solvers for PEP take time that is either exponential in the code length or in the dimension of the hull, which is the intersection between a code and its dual.
To avoid the latter type of attacks, PEP-based cryptosystems employ linear codes with... -
Aditya Khanna (Virginia Tech)5/20/26, 11:50 AM
Let $A = (A_n)_{n\geq 0}$ and $B = (B_n)_{n\geq 0}$ be families of "recursive'' rectangular matrices, that is, the entries of $A_n$ can be expressed as a linear combination of entries of $A_m$ for $m < n$, and similarly for $B$. Such families arise in algebraic combinatorics as change-of-basis matrices between the basis of symmetric functions and their generalizations. The entries of such...
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Siting Liu (University of California, Riverside)5/20/26, 11:50 AMAdvances in Randomized Algorithms and Kernel Methods for Rank-Structured MatricesMinisymposium Talk
We study mean-field games with nonlocal interactions modeled through kernel-based representations. Using feature-space expansions inspired by kernel methods, the resulting models admit a variational saddle-point formulation that is well suited for efficient primal–dual algorithms such as the primal-dual hybrid gradient method. We also discuss inverse problems in which interaction mechanisms...
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David Bindel (Cornell University)5/20/26, 11:50 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Stellarators are non-axisymmetric magnetic field configurations used to confine plasmas. Within a stellarator, particles roughly follow magnetic field lines, and the magnetic fields in stellarators can be organized into different regions according to the dynamics of field line flows, with regions of nested flux surfaces potentially interspersed with islands or regions of chaos. While can...
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Dacian Bonta (Emory University)5/20/26, 11:50 AM
The expectation maximization (EM) algorithm, widely used in medical image tomographic reconstruction, iteratively estimates the values of a discrete distribution of emission sources $\rho_{t=1,2,..,T}$ from a set of detector measurements $A_{k=1,2,..,K}$. The two steps of an iteration are:
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$A_k^{(n)} = \sum_{t} P_{k \leftarrow t} \cdot \rho_t^{(n)}$ (E) and $\rho_t^{(n+1)} = \rho_t^{(n)}... -
Ranveer Singh (IIT Indore, India)5/20/26, 11:50 AMApplication-Driven Family of Matrix Computations: Factorization, Inverse, Linear SolveMinisymposium Talk
The Moore-Penrose inverse of a Laplacian matrix is a fundamental object in algebraic graph theory and network analysis, but explicit formulas are known only for restricted graph families. In this paper, we study the Laplacian matrix of unicyclic graphs, and derive an explicit closed-form formula for the Moore-Penrose inverse which can be calculated in $O(n^2)$, where n is the size of the graph.
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Juan Felipe Osorio Ramirez (University of Washington)5/20/26, 11:50 AMTheoretical Advances in Operator LearningMinisymposium Talk
We present an alternative perspective on operator learning for problems in which the operator is implicitly defined by a partial differential equation. Rather than learning the solution operator directly as a high-dimensional mapping, we propose to first learn the underlying PDE operator as a local differential operator and then numerically invert it to evaluate the associated solution operator.
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Mary Flagg (University of St. Thomas)5/20/26, 11:50 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
Given a simple graph $G$, $\mathcal{S}(G)$ is the set of real symmetric matrices indexed by the vertices in $G$ and with off-diagonal zeros corresponding to non-edges in $G$. The problem of finding the maximum nullity of a matrix in $\mathcal{S}(G)$ has been extensively studied. We consider the maximum nullity of a matrix $A$ and its principal submatrix $A(i)$ corresponding to deleting the...
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Malena Espanol (Arizona State University)5/20/26, 11:50 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Separable nonlinear inverse problems arise in many applications where a forward model depends linearly on some unknowns and nonlinearly on others, including semi-blind deconvolution. We adopt a Bayesian framework with Gaussian noise and Gaussian priors on the linear variables, leading to regularized formulations of the inverse problem. We examine prior models for the nonlinear parameters and...
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5/21/26, 8:20 AM
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Sirani M. Perera (Embry-Riddle Aeronautical University, USA)5/21/26, 8:30 AM
Millimeter waves within the sub-terahertz band offer a plethora of applications in next-generation wireless communication. However, they also introduce severe real-time and hardware limitations, making conventional wideband multi-beam beamforming exceedingly complex. For example, an $N$-element array using true-time delay beamformers needs $\mathcal{O}(N^2)$ time delays or phase shifts, while...
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Chi-Kwong Li (College of William and Mary)5/21/26, 9:25 AM
The numerical range is a fundamental tool for understanding the properties of matrices and operators. In this talk, we discuss recent advances in the study of the numerical range and its generalizations, specifically focusing on their utility in analyzing operator dilations. We demonstrate how these theoretical frameworks provide critical insights into applied topics, including quantum...
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Namita Behera (Sikkim University)5/21/26, 11:00 AMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
Arithmetical structures on graphs have recently attracted considerable attention due to their rich connections with combinatorics, algebra, and graph theory. In this work, we undertake a detailed study of arithmetical structures on fan graphs. For a finite and connected graph G, an arithmetical structure is defined as a pair (d, r) of positive integer vectors such that the vector r is...
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Yang Liu (Lawrence Berkeley National Laboratory)5/21/26, 11:00 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
The development of hierarchical matrix techniques has been essential for many modern scientific computing frameworks including fast direct solvers for PDEs and integral equations, scalable kernel methods and Gaussian processes, and second-order optimization and inverse problems, etc. These algorithms oftentimes lead to optimal computational and memory complexities. That said, when dealing with...
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Dr Xiang Xiang Wang (Michigan State University)5/21/26, 11:00 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Single-cell data are typically represented in Euclidean space, which limits the ability to capture intrinsic correlations and multiscale geometric structure. We propose a multiscale framework based on Grassmann manifolds that represents single-cell RNA-seq data through subspace geometry across multiple scales.
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Sajal Ghosh (Indian Statistical Institute)5/21/26, 11:00 AM
It is well known that the success of Lemke's algorithm for solving a linear complementarity problem LCP(\textit{$q,M$}) depends on the matrix class \textit{$M$}. Many researchers investigated a large class of matrices that Lemke's algorithm can be used for solving. In this paper, we follow a different approach. First, we construct an artificial LCP$(\bar{q}_{1},\mathcal{M}_{1})$ from...
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Mr Tianchen Shao (Tsinghua University)5/21/26, 11:00 AMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
Electromagnetic inverse scattering in lossy media is challenging due to severe signal attenuation and broken time-reversal symmetry. We present an efficient permittivity inversion framework for inhomogeneous lossy media by extending the wave operator model. Under the Liouville transformation, electric field propagation is governed by $[\partial_t^2 + p(x)\partial_t + A] E = \partial_t f...
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Chelsea Drum (Emory University)5/21/26, 11:00 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In recent years, mixed-precision and reduced-precision algorithms for solving large-scale linear systems have emerged as an effective approach for exploiting modern GPU architectures. While much of this work has focused on well-conditioned systems, comparatively little attention has been given to ill-posed inverse problems, where regularization is essential. In this talk we consider projected...
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Robin Herkert (University of Stuttgart)5/21/26, 11:00 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Large-scale Hamiltonian dynamics are governed by
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$$ \dot x = J\nabla H(x),\quad J=\begin{bmatrix}0&I\\-I&0\end{bmatrix}, $$
and arise from spatial discretizations of conservative PDEs as well as in molecular and multibody models. In multi-query, control, and real-time settings, projection-based model order reduction (MOR) is essential, but generic reduced spaces may destroy the... -
Rodrigo San-José (Virginia Tech)5/21/26, 11:00 AM
The relative generalized Hamming weights of a nested pair of linear codes are a generalization of the minimum distance. We will see how these parameters characterize the security of ramp secret sharing schemes, and how this can be adapted for private information retrieval. The computation of these parameters for a linear code is NP-hard in general, and we will study the most efficient current...
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Caleb Cheung (University of Wyoming)5/21/26, 11:00 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
Let $A$ be an $m \times n$ matrix. The spoiler space of $A$ is the set of all $m\times n$ matrices $X$ such that, $XA^\top$ is symmetric, $A^\top X$ is symmetric, and $X\circ A = O$, where "$\circ$" denotes the entrywise Schur product. If the spoiler space of $A$ contains only the 0 matrix, we say that $A$ has the Strong Singular Value Property (SSVP). The SSVP gives us access to a rich...
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Jocelyn Chi (University of Minnesota Twin Cities)5/21/26, 11:00 AMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
The canonical polyadic (CP) tensor decomposition represents a multidimensional data array as a sum of rank-one outer products of latent factors. Building on CP-HiFi, the hybrid infinite- and finite-dimensional CP framework of Larsen et al. (2024), which introduces quasitensors by modeling selected modes as smooth functional factors in a reproducing kernel Hilbert space, we replace the standard...
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Charbel Abi Younes (University of Washington)5/21/26, 11:00 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
We introduce a new approach for estimating the asymptotic spectral distribution (ASD) of a random matrix using a single, sufficiently high-dimensional sample, without computing the full spectrum. The method builds on the Lanczos algorithm, together with asymptotic analysis and perturbation theory for orthogonal polynomials, and enables efficient and accurate estimation of the ASD. We...
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Dr Tianyun Tang (University of Chicago)5/21/26, 11:00 AM
We show that linearly constrained linear optimization over a Stiefel or Grassmann manifold is NP-hard in general. We show that the same is true for unconstrained quadratic opti- mization over a Stiefel manifold. We will show that unless P = NP, these optimization problems over a Stiefel manifold do not have FPTAS. As an aside we extend our results to flag manifolds. Combined with earlier...
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Heike Faßbender (TU Braunschweig, Institute for Numerical Analysis)5/21/26, 11:00 AMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
It is well known that the matrix exponential $\exp(H)$ is symplectic whenever
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$H \in \mathbb{R}^{2n \times 2n}$ is a Hamiltonian matrix. A matrix $H$ is called
Hamiltonian if it satisfies $HJ = (HJ)^{T},$
while a matrix $S$ is called symplectic (or $J$-orthogonal) if $S^{T} J S = J.$
Here, $J \in \mathbb{R}^{2n \times 2n}$ denotes $J =
\left [\begin{smallmatrix} 0 & I_n \ -I_n &... -
Prof. Lassi Roininen (LUT University)5/21/26, 11:25 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Edges in imaging, that is sharp discontinuities in intensity, pose a significant challenge for inverse problems algorithms that often rely on Gaussian assumptions. Non-Gaussian heavy-tailed priors, which can better model the sparsity and sharp transitions inherent in edges, offer an alternative for edge-preserving image reconstructions. We consider the inherent difficulties in handling edges...
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Adam Downs (Virginia Tech)5/21/26, 11:25 AM
Two linear codes are equivalent if there exists a monomial matrix that transforms one to the other. The problem of finding a monomial transformation from one code to another underlies the Linear Equivalence Signature Scheme (LESS). An automorphism of a linear code is a monomial matrix which fixes the code. When a code has a large number of automorphisms, it is easier to solve the linear...
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Tin-Yau Tam (University of Nevada, Reno)5/21/26, 11:25 AM
We present a differential--geometric view of the Schur--Horn theorem and related convexity phenomena. For an $n\times n$ Hermitian matrix $A$ with simple spectrum, the Schur--Horn map
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$$ \mu: {\mathrm U}(n) \to \mathbb R^n,\quad \mu(U)=\mathrm{diag}(UA U^{-1}), \qquad U\in {\mathrm U}(n), $$
is shown to be a proper submersion over the relative interior of the Schur--Horn polytope, where... -
Robin Armstrong (Cornell University)5/21/26, 11:25 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
Many algorithms in data assimilation and model order reduction rely on sample-based estimates for a covariance matrix associated with the trajectory of a high-dimensional dynamical system. The number of available samples is often far less than the dimension of the underlying state space because of computational constraints. Under these circumstances, extracting meaningful covariance...
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Michele Rinelli (KU Leuven)5/21/26, 11:25 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
The deep connection between Krylov methods, scalar orthogonal polynomials, and moment matrices is well established, particularly for Hermitian and unitary matrices. In this talk, we extend this framework to block Krylov methods and orthogonal matrix polynomials.
By representing the elements of a block Krylov subspace via matrix polynomials, we consider the matrix-valued inner product...
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Ahmed Salam (Université du Littoral-Côte d'Opale)5/21/26, 11:25 AMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
In the context of computations of eignevalues and eignevectors, structure-preserving of a class of specific structured matrices, the reduction of a matrix to a $J$-Hessenberg condensed form is needed.\
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Such reduction is based on symplectic similarity transformations.
It is a crucial step in the $SR$-algorithm (which is a $QR$-like algorithm), structure-preserving, for computing... -
Shweta Yadav (Shiv Nadar University)5/21/26, 11:25 AM
We investigate the structural properties of the solution set of absolute value equations (AVE) of the form $Ax - |x| = b$. Extending the seminal work of Hladík (SIAM J. Matrix Anal. Appl., 2023), we address his open questions originally posed for $Ax + |x| = b$ and establish analogous results for the alternative form considered here. Using the equivalence between AVE and the linear...
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Bibhas Adhikari (Fujitsu Research of America, Inc.)5/21/26, 11:25 AMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
We discuss a quantum-classical streaming algorithm that processes signed edges to efficiently estimate the counts of triangles of diverse signed configurations in the edge stream. The approach introduces a quantum sketch register for processing the signed-edge-stream, together with measurement operators for query-pair calls in the quantum estimator, while a complementary classical estimator...
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Katherine Pearce (Oden Institute, UT Austin)5/21/26, 11:25 AMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
Attention mechanisms are a central component of transformer models that capture contextual relationships between tokens in large language models. Although many of the underlying computations (e.g., query, key, and value embeddings in multi-head attention) are inherently multi-way, classical transformer models are built on matrix-based formulations.
In this talk, we discuss several ways that...
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Sarswati Shah5/21/26, 11:25 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
In this work, we propose a reduced-order modeling (ROM) framework for conservation laws that operates in the Cumulative Distribution Transform (CDT) domain. The CDT maps nonnegative, unit-mass states to an $L^2$ Hilbert space, in which pure translations become affine lines and $W_2$ (optimal transport) distances coincide with Euclidean distances. This linearization dramatically improves the...
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Andreas Tataris5/21/26, 11:25 AMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
We present a numerical method for solving an inverse boundary value problem of estimating the acoustic velocity in the Helmholtz equation from frequency domain measurements based on reduced order models (ROM). The ROM is the Galerkin projection of the Helmholtz operator onto a subspace spanned by its solution snapshots at certain wavenumbers. We show how to reconstruct the ROM in a data-driven...
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Mr Augustine (Runshi) Tang (University of Wisconsin-Madison)5/21/26, 11:25 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially...
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Himanshu Gupta (University of Regina)5/21/26, 11:25 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
Symplectic geometry appears in many areas of mathematics, physics, and applications, and naturally gives rise to interesting matrix families and properties. Symplectic eigenvalues extend the classical notion of eigenvalues to the symplectic setting and are guaranteed to exist for positive definite matrices by Williamson's theorem. We introduce the inverse symplectic eigenvalue problem for...
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Robbe Vermeiren (KU Leuven)5/21/26, 11:50 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Rational functions are fundamental to several non-linear approximation problems in, for example, model reduction, system identification, and PDE problems. Consequently, one is often interested in constructing an orthonormal basis of rational functions to ensure numerical stability and conditioning.
In this talk, we present a generalized framework for constructing such bases for rational...
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Dr Minerva Catral (Xavier University)5/21/26, 11:50 AMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
For vertex-labelled graphs $G$ and $H$ on $n\geq 1$ vertices, we consider matrices of the form $C(A,B) = \left[\begin{array}{c|c} A&B\\ \hline I&O\\\end{array}\right]\in\mathbb{R}^{2n\times 2n}$ where $A,B\in\mathbb{R}^{n\times n}$ are a pair of real symmetric matrices with nonzero patterns determined by the edges of the graph pair $G, H$. We denote the set of all such matrices by...
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Jorge Reyes (Virginia Tech)5/21/26, 11:50 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
This talk focuses on the numerical analysis of regularized projection-based reduced-order models (ROMs) for turbulent fluid flows. Direct numerical simulations are well known to be computationally infeasible for routine simulations in computational fluid dynamics, particularly at high Reynolds numbers. Reduced-order models offer an efficient low-dimensional framework capable of producing fast...
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Dr Karl Pierce (University of Maryland, College Park)5/21/26, 11:50 AMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
The CANDECOMP/PARAFAC (CP) decomposition is a powerful tool used for multiway data analysis and to break the “curse of dimensionality” associated with higher-order tensors. The most common way to compute the CP decomposition of a tensor is via a standard alternating least squares (CP-ALS) algorithm. With the CP-ALS, one must iteratively solve a set of overdetermined least squares problem which...
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Abraham Reyes Velazquez (University of Manchester)5/21/26, 11:50 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We propose a unified framework that allows for the full mechanistic reconstruction of chemical reaction networks (CRNs) from concentration data. The framework utilizes an integral formulation of the differential equations governing the chemical reactions, followed by an automatic procedure to recover admissible mass-action mechanisms from the equations. We provide theoretical justification...
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Deepa Sinha5/21/26, 11:50 AMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
A signed graph Σ is defined as an ordered pair (Σᵤ, σ), where Σᵤ = (V, E) is the underlying graph and σ is a signature mapping from the edge set E to {+, −}. A negative section of a signed graph Σ refers to a maximal connected edge-induced subgraph consisting solely of the negative edges of Σ. Let Tₙᵖ denote the collection of all unbalanced tricyclic signed graphs of order n ≥ 4 with p (1 ≤ p...
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Lina Simbaqueba (Universität Leipzig)5/21/26, 11:50 AM
Given a field $\mathbb{F}$ and a directed graph $G$ with vertex set $\{1, 2, \ldots, n\}$, we define the minrank $\text{mr}_F(G)$ to be the minimum rank over all matrices $M$ with nonzero diagonal such that $M(i,j) = 0$ whenever $ij$ is not a directed edge. In this talk, we will discuss the problem of minimizing $\text{mr}_F(G)$ over all tournaments on $n$ vertices, as well as the problem of...
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Abraham Khan (North Carolina State University)5/21/26, 11:50 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
Kernel matrices arising in applications such as Gaussian processes may not always admit a low-rank approximation. Important examples are kernel matrices induced by certain members of the Matérn family of covariance kernels, with smaller length scales and values of $\nu$. Still, they can often be approximated by a hierarchical matrix ($\mathcal{H}$-matrix or $\mathcal{H}^{2}$-matrix), which...
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Jörn Zimmerling (Uppsala University)5/21/26, 11:50 AMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
We consider an inverse scattering problem for monostatic synthetic aperture radar (SAR), where the goal is to estimate the wave speed in a heterogeneous, isotropic medium using measurements from a moving antenna. The forward map, derived from Maxwell’s equations, is inherently nonlinear, accounts for multiple scattering, and exhibits high-frequency oscillations that make traditional nonlinear...
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Wendi Gao5/21/26, 11:50 AM
The Matrix Equivalence Digital Signature (MEDS) is a code-based digital signature that was submitted to the NIST call for quantum-resistant protocols. It is currently considered as a candidate for building advanced group action signatures schemes.
The hard problem behind this digital signature is the Matrix Code Equivalence problem. Namely, given two matrix codes $C_1$ and $C_2$, suppose...
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Pálfia Miklós (Corvinus University of Budapest)5/21/26, 11:50 AM
In this talk we investigate zeros of nonlinear operators on the cone of positive definite operators over a Hilbert space. The unique zero of such nonlinear operators define means of positive definite operators. Moreover these nonlinear operators generate strictly exponentially contracting semigroups in some metric defined on positive operators. We survey recent results that establish the...
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Nicole Joy Datu (University of the Philippines Diliman)5/21/26, 11:50 AMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
Let $G$ be a matrix group over a field $\mathbb{F}$ and $\phi: M_n(\mathbb{F}) \rightarrow M_n(\mathbb{F})$ be a map such that $\phi(A) \in G$ for all $A \in G.$
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An element $A \in G$ is said to be $\phi-$reversible if there exists $P \in G$ such that $PAP^{-1}=\phi(A).$ If $P$ can be chosen to be an involution (i.e., $P^2=I),$ then $A$ is said to be strongly $\phi-$reversible. The... -
Dr Andrew McCormack (University of Alberta)5/21/26, 11:50 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Matrix or tensor data often has structured rows, columns, or more generally modes. In particular, a mode may have a natural ordering that can be leveraged to obtain parsimonious representations of the data. To this end, the concept of the nondecreasing (ND) rank is introduced in this talk. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each...
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Ela Đimoti (University of Zagreb)5/21/26, 2:00 PM
Dynamic Mode Decomposition (DMD) is a data-driven tool for capturing complex nonlinear dynamics. It can be used to identify, analyze and forecast dynamical systems $x_{k+1}=F(x_k)$ governed by an unknown or complex mapping $F$ using only observed snapshots $s_1,s_2,...,s_{n+1}$. If we denote $X := (s_1 \ s_2 \ \cdots \ s_n)$, $Y := (s_2 \ s_3 \ \cdots \ s_{n+1})$, finite-dimensional...
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Zichao Wendy DI (Argonne National Lab)5/21/26, 2:00 PMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
Ptychography is a powerful coherent diffraction imaging technique essential for reconstructing high-resolution, complex-valued images from intensity-only measurements. However, the reconstruction poses significant challenges due to its nonconvex and ill-posed nature. We propose a novel multilevel optimization framework emphasizing stochastic learning principles to efficiently address these...
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Andrea Baleani (Scuola Normale Superiore di Pisa)5/21/26, 2:00 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Appearing in a wide variety of applications, often in the context of discretized (fractional) differential and integral operators, Hierarchically Semiseparable (HSS) matrices have a number of attractive properties facilitating the development of fast algorithms [6,4].
For HSS matrices, the rank-structure is numerically preserved if $f(z)$ is well-approximated by a rational function. The...
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Erkki Somersalo (Case Western Reserve University)5/21/26, 2:00 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In this talk, we revisit the Bayesian inverse problems formalism in infinite-dimensional distribution spaces, where function evaluations are replaced by evaluations by test functions. It is shown that linear inverse problems can be formulated without a reference to any infinite-dimensional representation of the unknown, e.g., in terms of basis vectors, and therefore, the forward problem has a...
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Zhifeng Deng (Xiamen University)5/21/26, 2:00 PM
The special orthogonal group $\mathbb{SO}_n$ is a Lie group whose geometry and local structure are encoded by the exponential map on its Lie algebra $\mathbf{Skew}_n$, the set of skew-symmetric matrices. The associated inverse problem---the matrix logarithm---exhibits a highly nontrivial local diffeomorphism structure, and the notion of a nearby logarithm arises naturally as a local inverse of...
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Elena Cherkaev (University of Utah)5/21/26, 2:00 PMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
Reduced order modeling methods characterized by significant reduction of computational time without loss of accuracy are extremely valuable for solution of large scale forward and inverse problems. The talk discusses a group of model order reduction methods related to matrix rational function (and matrix Pade) approximations of the spectral representations arising in inverse problems. The...
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Dr Hein Van der Holst (Georgia State University)5/21/26, 2:00 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
For a multi-digraph $D$ with vertex-set $V=\{1,\ldots,n\}$ and arc-set $A$, let $Q(D)$ be the set of all real $n\times n$ matrices $A=[a_{i,j}]$ with $a_{i,j}\not=0$ if $i\not=j$ and there is a single arc from $i$ to $j$, $a_{i,j}\in \mathbb{R}$ if $i\not=j$ and there are multiple arcs from $i$ to $j$, $a_{i,j}=0$ if $i\not=j$ and there is no arc from $i$ to $j$, $a_{i,i}\not=0$ if there is no...
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Hemant Mishra (Indian Institute of Technology (ISM) Dhanbad)5/21/26, 2:00 PMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
Williamson's theorem states that if $A$ is a $2n \times 2n$ real symmetric positive definite matrix then there exists a $2n \times 2n$ real symplectic matrix $M$ such that $M^T A M=D \oplus D$, where $D$ is an $n \times n$ diagonal matrix with positive diagonal entries known as the symplectic eigenvalues of $A$. The theorem is known to be generalized to $2n \times 2n$ real symmetric positive...
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Pietro Paparella (University of Washington Bothell)5/21/26, 2:00 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
The longstanding nonnegative inverse eigenvalue problem (NIEP) is to determine which multisets of complex numbers occur as the spectrum of an entry-wise nonnegative matrix. Although there are some well-known necessary conditions, a solution to the NIEP is far from known.
An invertible matrix is called a Perron similarity if it diagonalizes an irreducible, nonnegative matrix. Johnson...
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Henrique Soares Assumpção e Silva (Universidade Federal de Minas Gerais)5/21/26, 2:00 PM
We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the...
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Mr Matt Burnham (Iowa State University)5/21/26, 2:00 PM
Given a real number $q$, the $q$-Laplacian of a graph $G$ is the matrix $A+qD$ where $A$ is the adjacency matrix and $D$ the diagonal degree matrix. If the edge set of $G$ can be partitioned into edge-disjoint copies of $K_t$, then $G$ is called $K_{t}$-decomposable.
In this talk, we generalize some results from a survey paper of Cvetković, Rowlinson, and Simić about the signless...
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Hanmeng Zhan (Worcester Polytechnic Institute)5/21/26, 2:00 PMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
A discrete quantum walk takes place on the arcs of a graph, and evolves according to a coin operator and a shift operator. One important task, given the underlying graph, is to construct quantum walks that start with a state localized at a vertex and get arbitrarily close to a state localized at another vertex. In this talk, I will show how different coin operators translate into different...
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Chenyang Cao (Purdue University)5/21/26, 2:00 PMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
This talk gives a superfast divide-and-conquer algorithm for computing the full singular value decomposition (SVD) of hierarchical rank-structured matrices with small off-diagonal ranks. The method achieves nearly linear complexity while delivering all singular values and singular vectors in structured forms. The structured representation of singular vectors enables near-linear operations with...
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Ms Yidan Mei (Yale University)5/21/26, 2:00 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Transform-based tensor products, including the T-product and its more general form, namely the higher-order tensor-tensor product, have been widely used in image processing, signal reconstruction, and robotics. While invertible transforms enable tensor computations to be carried out via matrix operations in the transform domain, the resulting storage and computational costs remain prohibitive...
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Cooper Simpson (University of Washington)5/21/26, 2:25 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
The Lanczos process is a well-known Krylov subspace method for the orthogonal tridiagonalization of a hermitian matrix $\mathbf{Z}$. Equipped with a suitable function $f$, Lanczos function approximation (LFA) can be used as a powerful tool for approximating the matrix-function $f(\mathbf{Z})$ or matrix-function-vector products $f(\mathbf{Z})\mathbf{\omega}$.
We discuss an application of LFA...
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Mitchell Scott (Emory University)5/21/26, 2:25 PMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
The column subset selection problem seeks to find a collection of the matrix columns that have similar spectral properties to the original matrix. Recently with the large amount of data available, many have turned to using randomization to reduce the problem's computation. While there have been many methods that motivate how to select these columns, they are just that--individual columns....
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Isabel Byrne (University of Delaware)5/21/26, 2:25 PM
In 1985, Brouwer and Mesner proved that the vertex-connectivity of a strongly regular graph equals its valency and the only disconnecting sets of this size are point neighborhoods. In 2009, Brouwer and Koolen generalized this result to distance-regular graphs. In 1996, Brouwer conjectured that the minimum size of a disconnecting set of vertices whose removal disconnects a connected strongly...
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Aleksandr Malyshev5/21/26, 2:25 PM
We want to compute a $T$-periodic symmetric solution $X(t)$ of a $T$-periodic differential matrix Riccati equation
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$-\dot{X}(t)=X(t)A(t)+A^T(t)X(t)-X(t)B(t)R^{-1}(t)B^T(t)X(t)+Q(t)$
such that all solutions of the feedback system $\dot{x} = [A(t)-B(t)R^{-1}(t)B^T(t)X(t)]x(t)$ are asymptotically stable, i.e. $\lim_{t\to\infty}x(t)=0$. The standard solvability condition for the matrix Riccati... -
Anna Ma (University of California, Irvine)5/21/26, 2:25 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Solving linear systems is a crucial subroutine and challenge in data science and scientific computing. Classical approaches to solving linear systems assume that data is readily available and sufficiently small to be stored in memory. However, in the large-scale data setting, data may be so large that only partitions (e.g., single rows/columns of the matrix/tensor) can be utilized at a time....
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Alexander Mamonov (University of Houston)5/21/26, 2:25 PMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. The traditional full waveform inversion (FWI) formulation estimates the unknown coefficients via minimization of the nonlinear, least squares data fitting objective function. For typical band-limited and high frequency data, this...
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Ludovick Bouthat (Université Laval)5/21/26, 2:25 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
Stochastic matrices are matrices with nonnegative entries whose rows each sum to $1$. When a matrix and its transpose are both stochastic, it is said to be \emph{doubly stochastic}. In 1938, Kolmogorov proposed the problem of characterizing the region of possible eigenvalues of an $n \times n$ stochastic matrix, and Karpelevich gave a complete description thirteen years later. This talk...
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Prof. Shariefuddin Pirzada (University of Kashmir)5/21/26, 2:25 PMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
Let $G(V,E)$ be a simple graph of order $n$, size $m$ and having the vertex set $V(G)=\{v_1, v_2, \dots, v_n\}$ and edge set $E(G)=\{e_1, e_2,\dots, e_m\}$. The adjacency matrix $A=(a_{ij})$ of $G$ is a $(0, 1)$-square matrix of order $n$ whose $(i,j)$-entry is equal to 1 if $v_i$ is adjacent to $v_j$ and equal to 0, otherwise. Let $D(G)={diag}(d_1, d_2, \dots, d_n)$ be the diagonal matrix...
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Dr Lizuo Liu (Dartmouth College)5/21/26, 2:25 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce only conservation or rely on prior knowledge of the governing equations, our method parameterizes the flux functions in a form that guarantees real...
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Dr Azam Mozaffarikhah (Virginia Tech, Department of Mathematics)5/21/26, 2:25 PM
Polynomial factorization is classically studied within commutative polynomial rings, where irreducibility is an intrinsic algebraic property. In this talk, we present a linear-algebraic approach to factorization via entangled polynomial rings, in which polynomials are represented by structured matrices and analyzed using tools from matrix theory.
By embedding a polynomial into a family of...
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Anmary Tonny (Indian Institute of Technology, Madras)5/21/26, 2:25 PMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
In 1936, J. Williamson introduced the Williamson’s normal form for 2n × 2n positive definite real matrices. It is the symplectic analogue of the spectral theorem for normal matrices. In 2019, B. V. R. Bhat and T. C. John proved the infinite-dimensional analogue of the Williamson’s normal form and in 2024, H. K. Mishra extended the Williamson’s normal form to 2n × 2n real symmetric matrices. In...
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Xiang Lu (University of Chicago)5/21/26, 2:25 PM
We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution matrices. We will show that $\text{SO}(n)$ is a product of two real Grassmannians, $\text{SU}(n)$ a product of four complex Grassmannians, and $\text{Sp}(2n,...
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Mark Hunnell (Winston-Salem State University)5/21/26, 2:25 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
The minimum rank of a graph $G$ of order $n$ is the smallest possible rank over all real symmetric $n\times n$ matrices $A$ whose $(i,j)$th entry, for $i\neq j$, is nonzero whenever $ij$ is an edge of $G$ and zero otherwise. We discuss some refinements of techniques currently in the literature to determine the minimum rank of a graph, some new tools to bound this value, and an approach for...
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Christopher Wang (Cornell University)5/21/26, 2:25 PMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
We describe a problem arising from operator learning for hyperbolic PDEs, in which one would like to recover an unknown, non-standard low-rank hierarchical partition of a linear operator using only input-output data, or, in the finite-dimensional case, matrix-vector products. We provide a solution to the operator learning problem by employing a continuous analogue of the randomized SVD (RSVD)...
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Dr Sandeep Kumar (Wilfrid Laurier University)5/21/26, 2:50 PMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
Signed graphs provide a natural framework for modeling systems with antagonistic or cooperative interactions and arise in areas such as network science, social dynamics, and quantum systems. A signed graph $\Sigma = (G,\sigma)$ consists of an underlying graph $G = (V,E)$ together with a signature $\sigma : E \to \{+,-\}$.
In this talk, we present a new perspective on the Cartesian product...
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Fernando Guevara Vasquez (University of Utah)5/21/26, 2:50 PMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
The response matrix of an electrical circuits composed of two kinds of passive elements (e.g. LC, RC, CL...) is a matrix-valued rational function of the frequency that associates time-harmonic voltages at some terminal nodes to time-harmonic currents. We present necessary conditions that must be satisfied by the response matrix. These conditions can be used to construct circuits whose response...
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Brando Vagenende (Department Business Technology and Operations, Data Analytics Laboratory, Vrije Universiteit Brussel (VUB))5/21/26, 2:50 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
This talk presents spectral properties of monotone stochastic matrices which are characterised by the fact that each row stochastically dominates the preceding one, and which arise in contexts such as intergenerational mobility, equal-input models, and credit-rating systems.
In analogy with the stochastic matrices, for the monotone stochastic matrices both the individual eigenvalues as the...
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Robert Webber (University of California San Diego)5/21/26, 2:50 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse. What happens if a partial Cholesky approximation is combined with a Vecchia approximation of the residual? We show how the sum can be rewritten as a Vecchia...
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Mark Kempton (Brigham Young University)5/21/26, 2:50 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
One of the most challenging aspects of graph inverse eigenvalue problems is knowing when a graph admits a matrix with few distinct eigenvalues. We will discuss results where we construct matrices with only two distinct eigenvalues corresponding to graphs that arise from various kinds of product structures. We will discuss also some directions for future work along these lines.
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Dr Andrea Arnold (Worcester Polytechnic Institute)5/21/26, 2:50 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Many applications in modern day science involve unknown system parameters that must be estimated from limited data. A subset of these problems involves parameters that vary with time but have unknown evolution models and cannot be directly observed. In this work, we formulate time-varying parameter estimation in deterministic dynamical systems as an interpolation problem, where the function...
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Nathan Henry (University of California, Berkeley)5/21/26, 2:50 PM
Multi-head self-attention is a fundamental building block of the transformer architecture in modern machine learning, enabling large language models and much of modern generative AI as we know it. However, some aspects of the self-attention function space remain poorly understood. In particular, its parameterization is non-unique: continuous families of unique weight matrices can induce the...
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Joonwon Seo (Georgia State University)5/21/26, 2:50 PM
This 20-minute contributed talk focuses on two properties introduced in recent work on matrix manifolds: the Row Equivalence Transversality Property (RETP) and the Column Equivalence Transversality Property (CETP).
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For an $ m \times n $ real matrix $ A $, RETP holds if the manifolds $ \{GA : G \in \mathrm{GL}(m, \mathbb{R})\} $ and $ Q(\mathrm{sgn}(A)) $ intersect transversally at $ ... -
Haixiao Wang (University of Wisconsin-Madison)5/21/26, 2:50 PMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
In modern machine learning applications, data matrices are always assumed to admit the signal-plus-noise structure. Typically, we assume that the spectra of signal and noise matrices are well-separated and that noise subspaces only produce a marginal influence. While these assumptions are readily verified for dense matrices via classical random matrix theory, real-world data is often sparse,...
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Jiayu Bian (KTH Royal Institute of Technology)5/21/26, 2:50 PM
Spectral clustering is a graph-based method for data partitioning, which relates a relaxed graph partitioning problem to the eigenvectors of the associated graph Laplacian; see, e.g., [Peng et al., SIAM J. Comput. 46(2):710–743, 2017]. Following the computation of these eigenvectors, a post-processing step is used to determine the final clustering. Typically, k-means is the standard choice of...
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V B Kiran Kumar (Cochin University of Science And Technology)5/21/26, 2:50 PMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
Williamson’s Normal form for real positive matrices of even order serves as a symplectic analogue to the spectral theorem for normal matrices. Recent developments in quantum information theory have propelled Williamson’s normal form into an active research area known as 'finite-dimensional symplectic spectral theory,' akin to traditional spectral theory and matrix analysis.
An...
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Dr Neriman Tokcan (University of Massachusetts Boston)5/21/26, 2:50 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
High-throughput genomics and omics technologies generate data with intrinsic multi-way structure arising from multiple samples, molecular features, experimental conditions, and biological contexts. Standard matrix-based methods often obscure this structure through flattening or aggregation. Tensor-based representations provide a natural mathematical framework for preserving and exploiting the...
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Vishal Gupta (University of Rochester)5/21/26, 2:50 PM
The second largest eigenvalue of a graph's adjacency matrix captures important structure and spectral properties including connectivity and expansion. From the Alon-Boppana theorem, we know that if $\theta<2\sqrt{k-1}$, then there are only finitely many $k$-regular graphs with the second largest eigenvalue at most $\theta$. This motivates the following natural question posed by Richey, Stover,...
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Dallin Seyfried (Brigham Young University)5/21/26, 3:15 PMThe Inverse Eigenvalue Problem of a Graph and Zero ForcingMinisymposium Talk
An isospectral reduction is a method of shrinking a large matrix into a smaller matrix while preserving properties of the original's spectrum. The inverse, an isospectral unfolding, takes a matrix of an isospectral reduction and expands it into a larger matrix that has that reduction. We present a system of nonlinear equations forming the foundation of general isospectral unfolding. Graphs...
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Evan Coleman (University of Mary Washington)5/21/26, 3:15 PMTopics in Randomized Numerical Linear AlgebraMinisymposium Talk
Asynchronous iterative methods, such as Asynchronous Jacobi, offer a promising mechanism for overcoming synchronization bottlenecks in massively parallel and heterogeneous computing environments. By allowing processing elements to update components using the latest available data without global barriers, these methods maximize computational throughput. However, asynchrony also makes...
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Mikhail Zaslavskiy (Southern Methodist University)5/21/26, 3:15 PMModel- and Data-driven Reduced-order Models and Their Applications in Inverse ProblemsMinisymposium Talk
The inverse scattering problem formulated for the Schrödinger operators arises in various fields, including quantum mechanics, radars, viscoelasticity, Biot problems, remote sensing, geophysical, and medical imaging. The goal of imaging is to find medium properties in the domain using near-field measured data. The model based nonlinear optimization which is the method of choice for the...
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William Martin (Worcester Polytechnic Institute)5/21/26, 3:15 PM
Delsarte theory has been extended to the study of subsets in an increasing variety of association schemes in recent years, with many different motivations and applications. Tools originally developed for the study of error-correcting codes in the Hamming scheme and combinatorial $t$-designs in the Johnson scheme apply equally well in association schemes with irrational eigenvalues. The goal...
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Brecht Verbeken (Vrije Universiteit Brussel)5/21/26, 3:15 PMEigenvalues of Nonnegative and Stochastic MatricesMinisymposium Talk
Karpelevich’s theorem describes the single-eigenvalue region
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$ \Theta_n=\{\lambda\in{\bf C}:\lambda\in\sigma(A)\ {\rm for\ some\ }A\in{\bf R}^{n\times n} \ {\rm row\mbox{-}stochastic}\}. $
The set of row-stochastic matrices is the polytope $\mathrm{conv}(V_n)$, where $V_n$ consists of the $n^n$
deterministic Markov kernels ($0$-$1$ matrices with exactly one $1$ in each row).
For a... -
Eric de Sturler (Virginia Tech)5/21/26, 3:15 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Big data applications are becoming ever more prominent, and in many applications we need to solve very large linear or nonlinear inverse problems while handling only a relatively small amount of data at a time. Moreover, we are interested in distributed, possibly asynchronous, algorithms that solve large problems while only exchanging limited information. We need algorithms that combine...
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Dr Carmeliza Navasca (University of Alabama at Birmingham)5/21/26, 3:15 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
We study optimal control problems arising from partial differential equations. More specifically, we look at the optimal control of Allen-Cahn Equation (ACE) with a source term. ACE is well known for modeling phase transitions and thus, has many applications, apart from physics (semiconductors), in biological systems, material science and image processing. ACE models cellular membranes which...
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Chris Camaño (Caltech)5/21/26, 3:15 PMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
In recent years, tensor network methods have garnered increased attention for modeling high dimensional quantum many body systems and for representing high dimensional functions with structured correlations.
A basic unresolved question is whether standard numerical linear algebra primitives, such as Krylov based iterative solvers, can be realized in matrix product state and matrix...
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Tiju Cherian John (BITS Pilani, K K Birla Goa Campus)5/21/26, 3:15 PMSymplectic Linear Algebra and ApplicationsMinisymposium Talk
Quantum Gaussian channels are fundamental models for communication and information processing in continuous-variable quantum systems. This work addresses both foundational aspects and physical implementation pathways for these channels. Firstly, we provide a rigorous, unified framework by formally proving the equivalence of three principal definitions of quantum Gaussian channels prevalent in...
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Rakesh Jana (Indian Institute of Technology Kharagpur)5/21/26, 3:20 PMSpectral Interlacing, Graph Learning, and Quantum Perspectives on Signed GraphsMinisymposium Talk
Let $G=(V,E)$ be a connected graph. For a nonempty subset $S \subseteq V$, the Steiner distance $\textrm{dist}^s_G(S)$ is defined as the minimum number of edges in a connected subgraph of $G$ containing $S$. When $|S|=2$, this coincides with the classical distance between two vertices. For a fixed $k \in \mathbb{N}$, let $\mathbb V_k$ denote the set of all $k$-element subsets of $V$. The...
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5/21/26, 4:15 PM
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5/22/26, 8:30 AM
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Mr Jingyu Liu (Fudan University)5/22/26, 8:45 AM
The nonuniform discrete Fourier transform (NUDFT) and its inverse are widely used in various fields of scientific computing. In this article, we propose a novel superfast direct inversion method for type-III NUDFT. The proposed method approximates the type-III NUDFT matrix as a product of a type-II NUDFT matrix and an HSS matrix, where the type-II NUDFT matrix is further decomposed into the...
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Lorenzo Lazzarino (University of Oxford)5/22/26, 8:45 AM
Randomized algorithms in numerical linear algebra have proven to be effective in ameliorating issues of scalability when working with large matrices, efficiently producing accurate low-rank approximations. A key remaining challenge, however, is to efficiently assess the approximation accuracy of randomized methods without additional expensive matrix accesses.
In this talk, we discuss a...
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Chao Chen (NC State)5/22/26, 8:45 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
Dense matrices arise in many areas of computational science, and hierarchical approximation methods have been developed to reduce their storage and computational costs. However, many existing approaches require access to individual matrix entries, which may not be available or prohibitively expensive to compute in important applications. A prominent example is the Hessian in Bayesian inverse...
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Freeman Slaughter (University of South Florida)5/22/26, 8:45 AM
Arithmetic circuits provide a versatile framework for demonstrating generic algebraic statements, expressible as a system of polynomials, in a zero-knowledge manner. While this primitive can be used to prove knowledge of solutions to NP-complete problems (graph 3-coloring, Sudoku, etc), existing implementations generally rely on discrete logarithm problem assumptions. In this talk, we...
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Paul Van Dooren (Universite catholique de Louvain)5/22/26, 8:45 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We show how to use tangential interpolation techniques to construct structured linearizations for several types of structured rational matrices. The classes studied in this paper are square rational matrices that are either Hermitian, or skew-Hermitian, or complex symmetric, or complex skew-symmetric, upon evaluation on one of the following three curves~: the real axis, the imaginary axis and...
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Jonathan Lindbloom (Dartmouth College)5/22/26, 8:45 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Hybrid projection methods are an effective iterative approach for the solution of large-scale linear inverse problems, including those promoting sparsity in the recovered solution. Priorconditioned (prior-preconditioned) hybrid methods have been proposed to improve performance, but introduce additional computational costs in each iteration related to the application of a weighted pseudoinverse...
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Jeff Borggaard (Virginia Tech)5/22/26, 8:45 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Multivariate polynomial approximations to Hamilton-Jacobi-Bellman equations can be expressed using Kronecker products leading to very large, but structured, linear systems. Their structure appears as n-way generalizations of Lyapunov or generalized Lyapunov equations. For monomial terms of degree d, their dimension scales as the number of state dimensions n raised to the d. For...
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Giacomo Antonioli (Universita di Pisa)5/22/26, 8:45 AM
We present a quantum framework for solving a large class of elliptic and parabolic Partial Differential Equations (PDEs) endowed with periodic conditions. We solve the Poisson equation $\Delta u = f$ and the heat equation on the $d$-dimensional flat torus using a Fourier spectral method implemented on quantum circuits.
The main contribution is an efficient use of block encoding to load the...
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Alexander Hsu (University of Washington)5/22/26, 8:45 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Computing the diagonal entries of a large linear operator is a common computational primitive in numerical linear algebra, with applications in uncertainty quantification, cross-validation, perturbation analysis, electronic structure calculation and more. However, estimating the diagonals of a matrix given only implicit matrix-vector access is challenging, as randomized algorithms suffer from...
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Anna Konstorum5/22/26, 9:10 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Symmetric tensor diagonalization has applications in statistics and signal processing. Unlike for real symmetric matrices, there is no guarantee that a real-valued symmetric tensor is diagonalizable. Therefore, one generally approaches the problem as an approximate tensor diagonalization (ATD) problem. In this talk, we show that Jacobi-type methods for ATD that naturally extend the Jacobi...
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Kate Wall (Tufts University)5/22/26, 9:10 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
A preconditioner for solving fractional partial differential equations (PDEs) is presented. In our method the fractional PDE is discretized on an adaptive grid, resulting in a Hierarchical matrix representation. The stiffness matrix has Toeplitz blocks along the diagonal and low-rank approximations off the diagonal. Our preconditioner expands on previously developed methods of conditioning...
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Hiram López (Virginia Tech)5/22/26, 9:10 AM
We introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or q-polymatroid (for a rank-metric code) associated to the code. By means of examples, we show that the code distances allow us to distinguish some inequivalent MDS or MRD...
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Mr Koushik Bhakta (Indian Institute of Technology Guwahati)5/22/26, 9:10 AM
In this work, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider the transfer of quantum states localized at the vertices of a graph and use Chebyshev polynomials to analyze PGST between such states. In general, we find a necessary and sufficient condition for the occurrence of PGST on graphs. We then focus our analysis on abelian Cayley graphs and derive a...
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Hrvoje Olić (Faculty of Science, University of Zagreb)5/22/26, 9:10 AM
The implicit trace estimation is a problem of approximating the trace of a matrix $A$ accessed only through matrix-vector multiplication $x \mapsto Ax$, with the goal of using as few multiplications as possible to obtain an accurate approximation. Girard-Hutchinson's estimator computes the $\varepsilon$-approximation using $\mathcal{O}(\varepsilon^{-2})$ products, while its' variance-reducing...
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Akwum Onwunta (Industrial and Systems Engineering Department, Lehigh University)5/22/26, 9:10 AM
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element discretization, stochastic Galerkin approximation, and advanced time-discretization schemes, the approach addresses the challenge of large-scale, ill-conditioned linear...
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Ion Victor Gosea (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany)5/22/26, 9:10 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We extend the Loewner framework to multivariate (static and dynamic) functions with an arbitrary number $n$ of variables [1]. We present the following facts:
(i) That $n$-variable rational functions (and realization), described in the barycentric basis, can be constructed to interpolate and/or approximate/compress any tensorized $n$-D data or $n$-variate function;
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(ii) That these... -
Raphael Meyer (UC Berkeley)5/22/26, 9:10 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
Solving linear systems Ax=b is a fundamental pillar of NLA. For over 60 years, iterative methods that access A only through matrix-vector products have been the standard approach for solving large linear systems. While lower bounds exist for many special cases, prior work has not shown that methods like GMRES and MINRES achieve an asymptotically optimal matrix-vector complexity for...
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Diego Arenas Mata (Virginia Tech)5/22/26, 9:10 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Sparse priors, such as the Laplace prior, are of considerable interest in Bayesian inverse problems because they promote sparsity and preserve edges in the solution, which are often more appropriate than the smooth reconstructions obtained with Gaussian priors. However, sampling from the resulting non-Gaussian posteriors is challenging, particularly in high-dimensional settings. To address...
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Misha Kilmer (Tufts University)5/22/26, 9:35 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Reconstructing high-quality images with sharp edges requires edge-preserving regularization, often imposed using the $\ell_1$-norm of the gradient. To get a computationally tractable problem, the $\ell_1$-norm term is typically replaced with a sequence of $\ell_2$-norm weighted gradient terms with the weights determined from the current solution estimate. The majorization-minimization...
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Ichitaro Yamazaki (Sandia Labs)5/22/26, 9:35 AMHierarchical Low-Rank Approximations: Algorithms and ApplicationsMinisymposium Talk
We discuss the adaptive coarse-space basis functions for the multi-level overlapping additive Schwarz preconditioners implemented in FROSch. The basis functions are formed based on the discrete Harmonic extensions of the local subdomain interface functions. The basis functions for the interface are composed of the eigenvectors corresponding to the small eigenvalues of the generalized...
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William Mahaney (Virginia Tech)5/22/26, 9:35 AM
Goppa codes form a structured family of linear error-correcting codes introduced by Valery D. Goppa in 1970 and later interpreted within the framework of algebraic geometry as codes arising from algebraic curves over finite fields. Binary Goppa codes with irreducible Goppa polynomials are used in the Classic McEliece post-quantum key encapsulation mechanism (PQ-KEM), where their efficient...
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Steffen W. R. Werner (Virginia Tech)5/22/26, 9:35 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Learning dynamical systems from data has emerged as a pivotal area of research, bridging the realms of mathematics, engineering, and data science. Of particular importance is the construction of models with meaningful internal structure that allows interpretability and explainability of the results. In the case of mechanical and electro-mechanical processes, dynamical systems are typically...
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Andrew Higgins (Sandia National Laboratories)5/22/26, 9:35 AMPolynomials, Krylov Methods and ApplicationsMinisymposium Talk
We integrate random sketching techniques into block orthogonalization schemes needed for $s$-step GMRES. The resulting one-stage and two-stage block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank.
We implement these randomized block...
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Matthew Park (Virginia Tech)5/22/26, 9:35 AM
Symplectic linear algebra has had profound connections in many areas of math and physics. Despite this, the subject remains outside the scope of standard linear algebra education. In this talk, I propose motivating the subject via the study of complex coordinate space as the canonical symplectic vector space and argue its approachability for an undergraduate audience. I argue this by...
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Sherry Li (LBNL)5/22/26, 10:45 AM
Hierarchically low-rank (H-LR) matrices have been widely used to design fast solvers for integral equations, boundary element methods, discretized PDEs, and kernel matrices in statistical and machine learning. The computational bottleneck in these solvers is often the construction algorithm which converts a standard dense matrix into an H-LR format. We will present two types of algorithms for...
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John Urschel (MIT)5/22/26, 11:40 AM
Given a symmetric matrix with a given sign pattern, what can the sign patterns of its eigenvectors look like? This simple question is closely related to the study of discrete nodal statistics, and draws strong parallels with classical results in analysis for Laplacian eigenfunctions. In this talk, we will give an overview of the field, covering key results on nodal sets for graphs and their...
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5/22/26, 12:30 PM
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