A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices
Numerical Analysis
2020-11-04 v3 Numerical Analysis
Abstract
Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix function of a large Hermitian matrix on a vector. Using new error bounds and estimates, as well as existing results, we derive predictions of the practical performance of the methods, and rank them accordingly. As by-products, we derive new results on inexact Krylov iterations for matrix functions in order to allow for a fair comparison of rational Krylov methods with polynomial inner solves.
Keywords
Cite
@article{arxiv.2006.05922,
title = {A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices},
author = {Stefan Güttel and Marcel Schweitzer},
journal= {arXiv preprint arXiv:2006.05922},
year = {2020}
}