Residual iterative schemes for large-scale nonsymmetric positive definite linear systems
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200003 |
Resumo: | A new iterative scheme that uses the residual vector as search direction is proposed and analyzed for solving large-scale nonsymmetric linear systems, whose matrix has a positive (or negative) definite symmetric part. It is closely related to Richardson's method, although the stepsize and some other new features are inspired by the success of recently proposed residual methods for nonlinear systems. Numerical experiments are included to show that, without preconditioning, the proposed scheme outperforms some recently proposed variations on Richardson's method, and competes with well-known and well-established Krylov subspace methods: GMRES and BiCGSTAB. Our computational experiments also show that, in the presence of suitable preconditioning strategies, residual iterative methods can be competitive, and sometimes advantageous, when compared with Krylov subspace methods. |
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Computational & Applied Mathematics |
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Residual iterative schemes for large-scale nonsymmetric positive definite linear systemslinear systemsRichardson's methodKrylov subspace methodsspectral gradient methodA new iterative scheme that uses the residual vector as search direction is proposed and analyzed for solving large-scale nonsymmetric linear systems, whose matrix has a positive (or negative) definite symmetric part. It is closely related to Richardson's method, although the stepsize and some other new features are inspired by the success of recently proposed residual methods for nonlinear systems. Numerical experiments are included to show that, without preconditioning, the proposed scheme outperforms some recently proposed variations on Richardson's method, and competes with well-known and well-established Krylov subspace methods: GMRES and BiCGSTAB. Our computational experiments also show that, in the presence of suitable preconditioning strategies, residual iterative methods can be competitive, and sometimes advantageous, when compared with Krylov subspace methods.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=S1807-03022008000200003Computational & Applied Mathematics v.27 n.2 2008reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052008000200003info:eu-repo/semantics/openAccessLa Cruz,WilliamRaydan,Marcoseng2008-07-21T00:00:00Zoai:scielo:S1807-03022008000200003Revistahttps://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 |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
title |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
spellingShingle |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems La Cruz,William linear systems Richardson's method Krylov subspace methods spectral gradient method |
title_short |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
title_full |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
title_fullStr |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
title_full_unstemmed |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
title_sort |
Residual iterative schemes for large-scale nonsymmetric positive definite linear systems |
author |
La Cruz,William |
author_facet |
La Cruz,William Raydan,Marcos |
author_role |
author |
author2 |
Raydan,Marcos |
author2_role |
author |
dc.contributor.author.fl_str_mv |
La Cruz,William Raydan,Marcos |
dc.subject.por.fl_str_mv |
linear systems Richardson's method Krylov subspace methods spectral gradient method |
topic |
linear systems Richardson's method Krylov subspace methods spectral gradient method |
description |
A new iterative scheme that uses the residual vector as search direction is proposed and analyzed for solving large-scale nonsymmetric linear systems, whose matrix has a positive (or negative) definite symmetric part. It is closely related to Richardson's method, although the stepsize and some other new features are inspired by the success of recently proposed residual methods for nonlinear systems. Numerical experiments are included to show that, without preconditioning, the proposed scheme outperforms some recently proposed variations on Richardson's method, and competes with well-known and well-established Krylov subspace methods: GMRES and BiCGSTAB. Our computational experiments also show that, in the presence of suitable preconditioning strategies, residual iterative methods can be competitive, and sometimes advantageous, when compared with Krylov subspace methods. |
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=S1807-03022008000200003 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200003 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0101-82052008000200003 |
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 |
_version_ |
1754734890162585600 |