Randomized Low-Rank Approximation of Monotone Matrix Functions

DOI10.1137/22m1523923zbMath1515.65104arXiv2209.11023MaRDI QIDQ6166056

Daniel Kressner, David Persson

Publication date: 6 July 2023

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

Full work available at URL: https://arxiv.org/abs/2209.11023

zbMATH Keywords

matrix functionslow-rank approximationrandomized numerical linear algebra

Mathematics Subject Classification ID

Numerical computation of matrix exponential and similar matrix functions (65F60) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items (1)

Krylov-Aware Stochastic Trace Estimation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Extension of Rotfel'd Theorem
• Improved bounds on sample size for implicit matrix trace estimators
• A numerical study of large sparse matrix exponentials arising in Markov chains.
• Comparison of norms \(|||f(A)-f(B)|||\) and \(|||f(|A-B|)|||\)
• Randomized block Krylov subspace methods for trace and log-determinant estimators
• An estimator for the diagonal of a matrix
• Randomized matrix-free trace and log-determinant estimators
• On randomized trace estimates for indefinite matrices with an application to determinants
• Monte Carlo estimators for the Schatten \(p\)-norm of symmetric positive semidefinite matrices
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Inverse problems: A Bayesian perspective
• A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification
• Numerical Methods for Large Eigenvalue Problems
• Network Properties Revealed through Matrix Functions
• Randomization and Reweighted $\ell_1$-Minimization for A-Optimal Design of Linear Inverse Problems
• Assessing Stochastic Algorithms for Large Scale Nonlinear Least Squares Problems Using Extremal Probabilities of Linear Combinations of Gamma Random Variables
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Fast Estimation of $tr(f(A))$ via Stochastic Lanczos Quadrature
• Faster Kernel Ridge Regression Using Sketching and Preconditioning
• Practical Sketching Algorithms for Low-Rank Matrix Approximation
• Randomized Subspace Iteration: Analysis of Canonical Angles and Unitarily Invariant Norms
• Sharper Bounds for Regularized Data Fitting
• Improved Variants of the Hutch++ Algorithm for Trace Estimation
• Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM
• Randomized methods for matrix computations
• Functions of Matrices
• Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix

This page was built for publication: Randomized Low-Rank Approximation of Monotone Matrix Functions