Speeding Up Krylov Subspace Methods for Computing \(\boldsymbol{{f}(A){b}}\) via Randomization

DOI10.1137/22m1543458arXiv2212.12758MaRDI QIDQ6195017

Daniel Kressner, Alice Cortinovis, Yuji Nakatsukasa

Publication date: 16 February 2024

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

Full work available at URL: https://arxiv.org/abs/2212.12758

zbMATH Keywords

sketchingKrylov subspace methodrandomized algorithmsmatrix functionsleast-squares problemnonorthonormal basis

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

• Unnamed Item
• Unnamed Item
• A generalization of the steepest descent method for matrix functions
• ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
• Network Properties Revealed through Matrix Functions
• Deflated Restarting for Matrix Functions
• IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
• Fast Computation of the Matrix Exponential for a Toeplitz Matrix
• Blendenpik: Supercharging LAPACK's Least-Squares Solver
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• A Schur-Parlett Algorithm for Computing Matrix Functions
• Stability of the Lanczos Method for Matrix Function Approximation
• Decay Properties of Spectral Projectors with Applications to Electronic Structure
• Low-Rank Updates of Matrix Functions II: Rational Krylov Methods
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions
• Functions of Matrices
• Randomized Gram--Schmidt Process with Application to GMRES
• Randomized numerical linear algebra: Foundations and algorithms

This page was built for publication: Speeding Up Krylov Subspace Methods for Computing \(\boldsymbol{{f}(A){b}}\) via Randomization