A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods

Detalhes bibliográficos
Autor(a) principal: Gomes-Ruggiero,Márcia A.
Data de Publicação: 2008
Outros Autores: Lopes,Véra L. Rocha, Toledo-Benavides,Julia V.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200004
Resumo: Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the proposed modified GMRES(m) procedure for solving linear systems and also as part of an inexact Newton procedure, demonstrate the efficiency of this strategy.
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spelling A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methodslinear systemsrestarting GMRESinexact Newton methodnonlinear systemsRestarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the proposed modified GMRES(m) procedure for solving linear systems and also as part of an inexact Newton procedure, demonstrate the efficiency of this strategy.Sociedade Brasileira de Matemática Aplicada e Computacional2008-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200004Computational & Applied Mathematics v.27 n.2 2008reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052008000200004info:eu-repo/semantics/openAccessGomes-Ruggiero,Márcia A.Lopes,Véra L. RochaToledo-Benavides,Julia V.eng2008-07-21T00:00:00Zoai:scielo:S1807-03022008000200004Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2008-07-21T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
title A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
spellingShingle A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
Gomes-Ruggiero,Márcia A.
linear systems
restarting GMRES
inexact Newton method
nonlinear systems
title_short A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
title_full A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
title_fullStr A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
title_full_unstemmed A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
title_sort A safeguard approach to detect stagnation of GMRES(m) with applications in Newton-Krylov methods
author Gomes-Ruggiero,Márcia A.
author_facet Gomes-Ruggiero,Márcia A.
Lopes,Véra L. Rocha
Toledo-Benavides,Julia V.
author_role author
author2 Lopes,Véra L. Rocha
Toledo-Benavides,Julia V.
author2_role author
author
dc.contributor.author.fl_str_mv Gomes-Ruggiero,Márcia A.
Lopes,Véra L. Rocha
Toledo-Benavides,Julia V.
dc.subject.por.fl_str_mv linear systems
restarting GMRES
inexact Newton method
nonlinear systems
topic linear systems
restarting GMRES
inexact Newton method
nonlinear systems
description Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the proposed modified GMRES(m) procedure for solving linear systems and also as part of an inexact Newton procedure, demonstrate the efficiency of this strategy.
publishDate 2008
dc.date.none.fl_str_mv 2008-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200004
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200004
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-82052008000200004
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.27 n.2 2008
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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