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Stephen Thomas (Lehigh University)5/18/26, 3:45 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
For nonsymmetric operators, GMRES convergence is governed not only by the eigenvalues but also by the field of values and the resolvent norm. Non-normality amplifies the resolvent $||(zI - A)^{-1}||$ far from the spectrum, and the spectral geometry of the numerical range $W(A)$ determines how rapidly GMRES residual polynomials can decrease. The intrinsic information dimension $K_\infty$, a...
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Yunhui He (University of Houston)5/18/26, 4:10 PMAdvanced 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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Tom Werner (TU Braunschweig)5/18/26, 4:35 PMAdvanced 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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Maria Vasilyeva5/18/26, 5:00 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
We present a dynamic local–global coupling strategy for non-isothermal multiphase reactive flow in hydrate-bearing sediments, where hydrate phase change strongly couples transport, pressure, and temperature through variations in porosity and permeability. The nonlinear system is solved by sequential Picard iterations with physics-based splitting into transport, flow, and heat processes. To...
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Chen Greif (The Department of Computer Science)5/19/26, 11:00 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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Xingjie Li (UNC Charlotte)5/19/26, 11:25 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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Andreas Mang (Department of Mathematics, University of Houston)5/19/26, 11:50 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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Elle Buser (Emory University)5/19/26, 3:45 PMAdvanced Acceleration and Convergence Techniques for Solving Linear and Nonlinear SystemsMinisymposium Talk
We propose a natural gradient descent (NGD) method for efficient hyperparameter estimation in Bayesian inverse problems. In this framework, the objective is formulated as a function of a symmetric positive definite (SPD) matrix that depends on the hyperparameters. Rather than optimizing purely in the parameter space, we define a natural gradient that incorporates information about the model...
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Zequn Zheng (Louisiana State University)5/19/26, 4:10 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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Yunhui He (University of Houston)5/19/26, 4:35 PMAdvanced 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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Raymond Tuminaro (Sandia National Laboratories)5/19/26, 5:00 PMAdvanced 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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