Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14591
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Main Title: Spectral error bounds for Hermitian inexact Krylov methods
Author(s): Kandler, Ute
Christian, Schröder
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15818
http://dx.doi.org/10.14279/depositonce-14591
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We investigate the convergence behavior of inexact Krylov methods for the approximation of a few eigenvectors or invariant subspaces of a large, sparse Hermitian matrix. Bounds on the distance between an exact invariant subspace and a Krylov subspace and between an exact invariant subspace and a Ritz space are presented. Using the first bound we analyze the question: if a few iteration steps have been taken without convergence, how many more iterations have to be performed to achieve a preset tolerance. The second bound provides a measure on the approximation quality of a computed Ritz space. Traditional bounds of these quantities are particularly sensitive to the gap between the wanted eigenvalues and the remaining spectrum. Here this gap is allowed to be small by considering how well the exact invariant subspace is contained in a slightly larger approximated invariant subspace. Moreover, numerical experiments confirm the applicability of the given bounds.
Subject(s): Hermitian eigenvalue problem
inexact Krylov method
convergence analysis
Krylov relation
Ritz pair
Issue Date: 1-Jul-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
65G99 None of the above, but in this section
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 11
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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