Randomized block Krylov space methods for trace and log-determinant estimators
Numerical Analysis
2020-03-03 v1 Numerical Analysis
Abstract
We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we provide the error analysis of the proposed estimators and obtain the expectation and concentration error bounds. These bounds improve the corresponding ones given in the literature. Numerical experiments are presented to illustrate the performance of the algorithms and to test the error bounds.
Cite
@article{arxiv.2003.00212,
title = {Randomized block Krylov space methods for trace and log-determinant estimators},
author = {Hanyu Li and Yuanyang Zhu},
journal= {arXiv preprint arXiv:2003.00212},
year = {2020}
}