Randomized block Krylov subspace methods for trace and log-determinant estimators

DOI10.1007/s10543-021-00850-7OpenAlexW3138124916MaRDI QIDQ2045172

Yuanyang Zhu, Hanyu Li

Publication date: 12 August 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.00212

zbMATH Keywords

Chebyshev polynomialsrandomized algorithmKrylov subspace methodtrace estimatorlog-determinant estimator

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Approximation algorithms (68W25) Randomized algorithms (68W20)

Related Items (2)

Krylov-Aware Stochastic Trace Estimation ⋮ Randomized Low-Rank Approximation of Monotone Matrix Functions

Uses Software

• mctoolbox
• Krylstat

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Convergence of the block Lanczos method for eigenvalue clusters
• Randomized estimation of spectral densities of large matrices made accurate
• Improved bounds on sample size for implicit matrix trace estimators
• Parameter estimation in high dimensional Gaussian distributions
• Log-det approximation based on uniformly distributed seeds and its application to Gaussian process regression
• Chebyshev approximation of log-determinants of spatial weight matrices
• Schur complements and statistics
• Monte Carlo estimates of the log determinant of large sparse matrices
• Randomized LU decomposition using sparse projections
• Single-pass randomized algorithms for LU decomposition
• A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix
• Randomized matrix-free trace and log-determinant estimators
• A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices
• Improved Matrix Algorithms via the Subsampled Randomized Hadamard Transform
• A Matrix-free Approach for Solving the Parametric Gaussian Process Maximum Likelihood Problem
• Numerical Methods for Large Eigenvalue Problems
• Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
• IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
• Low-Rank Approximation and Regression in Input Sparsity Time
• Approximate implementation of the logarithm of the matrix determinant in Gaussian process regression
• Numerical methods for experimental design of large-scale linear ill-posed inverse problems
• Efficient Randomized Algorithms for the Fixed-Precision Low-Rank Matrix Approximation
• Accuracy and Stability of Numerical Algorithms
• Matrix decompositions using sub-Gaussian random matrices
• Subspace Iteration Randomization and Singular Value Problems
• Approximating Spectral Sums of Large-Scale Matrices using Stochastic Chebyshev Approximations
• Structural Convergence Results for Approximation of Dominant Subspaces from Block Krylov Spaces
• A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines

This page was built for publication: Randomized block Krylov subspace methods for trace and log-determinant estimators