-
Wasin So (San Jose State University)5/18/26, 2:00โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Victor Pan (City University of New York)5/18/26, 2:00โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Jitul Talukdar (IIT Kharagpur)5/18/26, 2:25โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Victor Pan (City University of New York)5/18/26, 2:25โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Joonwon Seo (Georgia State University)5/18/26, 2:50โฏPMContributed TalksContributed Talk
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).
Go to contribution page
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 $ ... -
Lauri Nyman (University of Manchester)5/18/26, 3:45โฏPMContributed TalksContributed Talk
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.
Go to contribution page -
Kyle Monette (University of Rhode Island)5/18/26, 4:10โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Antti Hannukainen (Aalto University)5/18/26, 4:35โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Paul Zachlin (Lakeland Community College)5/18/26, 5:00โฏPMContributed TalksContributed Talk
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.
Go to contribution page -
Eugenio Turchet (GSSI)5/19/26, 11:00โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
Shweta Yadav (Shiv Nadar University)5/19/26, 11:00โฏAMContributed TalksContributed Talk
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 Hladรญk (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...
Go to contribution page -
Lucas Siviero Sibemberg (UFRGS)5/19/26, 11:25โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
Dacian Bonta (Emory University)5/19/26, 11:25โฏAMContributed TalksContributed Talk
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:
Go to contribution page
$A_k^{(n)} = \sum_{t} P_{k \leftarrow t} \cdot \rho_t^{(n)}$ (E) and $\rho_t^{(n+1)} = \rho_t^{(n)}... -
Jonathan Tabares (Florida International University)5/19/26, 11:50โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
Peter Semrl (Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia)5/19/26, 2:00โฏPMContributed TalksContributed Talk
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.
Go to contribution page -
Dr Azam Mozaffarikhah (Virginia Tech, Department of Mathematics)5/19/26, 2:25โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Mr Koushik Bhakta (Indian Institute of Technology Guwahati)5/19/26, 2:50โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Etna Lindy (Aalto University)5/19/26, 3:45โฏPMContributed TalksContributed Talk
In the talk, I will go through our recent work regarding the Smith form of the Sylvester and Bรฉzout 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...
Go to contribution page -
Steve Mackey (Western Michigan University)5/19/26, 4:10โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Gustaf Lorentzon (KTH)5/19/26, 4:35โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Lorenzo Lazzarino (University of Oxford)5/21/26, 11:00โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
Hrvoje Oliฤ (Faculty of Science, University of Zagreb)5/21/26, 11:25โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
DuBose Tuller5/21/26, 2:00โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Michael Overton (New York University)5/21/26, 2:00โฏPMContributed TalksContributed Talk
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.
Go to contribution page -
Mr Jingyu Liu (Fudan University)5/21/26, 2:25โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
David S Watkins (Washington State University)5/21/26, 2:25โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Giacomo Antonioli (Universita di Pisa)5/21/26, 2:50โฏPMContributed TalksContributed Talk
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...
Go to contribution page -
Ela ฤimoti (University of Zagreb)5/22/26, 8:45โฏAMContributed TalksContributed Talk
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...
Go to contribution page -
Aleksandr Malyshev5/22/26, 9:10โฏAMContributed TalksContributed Talk
We want to compute a $T$-periodic symmetric solution $X(t)$ of a $T$-periodic differential matrix Riccati equation
Go to contribution page
$-\dot{X}(t)=X(t)A(t)+A^T(t)X(t)-X(t)B(t)R^{-1}(t)B^T(t)X(t)+Q(t)$
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... -
Jiayu Bian (KTH Royal Institute of Technology)5/22/26, 9:35โฏAMContributed TalksContributed Talk
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):710โ743, 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...
Go to contribution page
Choose timezone
Your profile timezone: