Expressions and bounds for the GMRES residual
type: Item
instance of: scholarly article
title: Expressions and bounds for the GMRES residual
zbMATH Open document ID: 0962.65030
DOI: 10.1023/A:1022371814205
published in: BIT
publication date: 2001-05-31T00:00:00Z
review text: The author discusses the generalized minimal residual method (GMRES) for the iterative solution of a linear system and derives expressions and bounds for the residual norm in this algorithm. The minimal residual norm is expressed in terms of the pseudo-inverse of the next Krylov matrix. The minimal residual norm of a scaled Jordan block is expressed in terms of the eigenvalues and deviation from normality. For normal matrices,the minimal residual norm is expressed in terms of products of the relative eigenvalue differences.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1533021
zbMATH Keywords: generalized minimal residual method
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: GMRES
zbMATH Keywords: algorithm
zbMATH Keywords: Vandermonde matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: departure from normality
zbMATH Keywords: normal matrices
author: Ilse C. F. Ipsen
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: a:1022371814205
OpenAlex ID: W1586935952
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description: scientific article; zbMATH DE number 1533021