Generalized line criterion for Gauss-Seidel method

Detalhes bibliográficos
Autor(a) principal: Garcia,M.V.P.
Data de Publicação: 2003
Outros Autores: Humes Jr.,C., Stern,J.M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100006
Resumo: We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems.
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spelling Generalized line criterion for Gauss-Seidel methodGauss-Seidel methodline criterionstability and control of manufacturing systemsWe present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems.Sociedade Brasileira de Matemática Aplicada e Computacional2003-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100006Computational & Applied Mathematics v.22 n.1 2003reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessGarcia,M.V.P.Humes Jr.,C.Stern,J.M.eng2004-07-19T00:00:00Zoai:scielo:S1807-03022003000100006Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2004-07-19T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Generalized line criterion for Gauss-Seidel method
title Generalized line criterion for Gauss-Seidel method
spellingShingle Generalized line criterion for Gauss-Seidel method
Garcia,M.V.P.
Gauss-Seidel method
line criterion
stability and control of manufacturing systems
title_short Generalized line criterion for Gauss-Seidel method
title_full Generalized line criterion for Gauss-Seidel method
title_fullStr Generalized line criterion for Gauss-Seidel method
title_full_unstemmed Generalized line criterion for Gauss-Seidel method
title_sort Generalized line criterion for Gauss-Seidel method
author Garcia,M.V.P.
author_facet Garcia,M.V.P.
Humes Jr.,C.
Stern,J.M.
author_role author
author2 Humes Jr.,C.
Stern,J.M.
author2_role author
author
dc.contributor.author.fl_str_mv Garcia,M.V.P.
Humes Jr.,C.
Stern,J.M.
dc.subject.por.fl_str_mv Gauss-Seidel method
line criterion
stability and control of manufacturing systems
topic Gauss-Seidel method
line criterion
stability and control of manufacturing systems
description We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss-Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the ''most general'' module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems.
publishDate 2003
dc.date.none.fl_str_mv 2003-01-01
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=S1807-03022003000100006
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100006
dc.language.iso.fl_str_mv eng
language eng
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.22 n.1 2003
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)
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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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