A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices

Güttel, Stefan and Schweitzer, Marcel (2020) A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 11 Jun 2020 23:23
Last Modified: 11 Jun 2020 23:23
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2769

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