Randomized Sketching for Krylov Approximations of Large-Scale Matrix Functions

DOI10.1137/22m1518062zbMath1520.65029arXiv2208.11447MaRDI QIDQ6116663

Stefan Güttel, Marcel Schweitzer

Publication date: 16 August 2023

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.11447

zbMATH Keywords

sketchingrandomizationGMRESmatrix functionKrylov methodFOM

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Randomized algorithms (68W20) Numerical computation of matrix exponential and similar matrix functions (65F60)

Cites Work

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• A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions
• On the generation of Krylov subspace bases
• A generalization of the steepest descent method for matrix functions
• Implementation of a restarted Krylov subspace method for the evaluation of matrix functions
• A fast randomized algorithm for the approximation of matrices
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds
• KIOPS: a fast adaptive Krylov subspace solver for exponential integrators
• Randomized linear algebra for model reduction. II: Minimal residual methods and dictionary-based approximation
• Randomized linear algebra for model reduction. I. Galerkin methods and error estimation
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
• Computational Advertising: Techniques for Targeting Relevant Ads
• A restarted Lanczos approximation to functions of a symmetric matrix
• A fast randomized algorithm for overdetermined linear least-squares regression
• Deflated Restarting for Matrix Functions
• On Restart and Error Estimation for Krylov Approximation of $w=f(A)v$
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory
• Fast CG-Based Methods for Tikhonov--Phillips Regularization
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• A Comparison of Limited-memory Krylov Methods for Stieltjes Functions of Hermitian Matrices
• Convergence of Restarted Krylov Subspace Methods for Stieltjes Functions of Matrices
• Approximating the Matrix Exponential of an Advection-Diffusion Operator Using the Incomplete Orthogonalization Method
• A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions
• Functions of Matrices
• Preconditioning Lanczos Approximations to the Matrix Exponential
• Some Remarks on the Elman Estimate for GMRES
• Two polynomial methods of calculating functions of symmetric matrices
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems
• Randomized Gram--Schmidt Process with Application to GMRES
• Multigrid preconditioning for the overlap operator in lattice QCD

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