Updating preconditioners for modified least squares problems

[EN] In this paper, we analyze how to update incomplete Cholesky preconditioners to solve least squares problems using iterative methods when the set of linear relations is updated with some new information, a new variable is added or, contrarily, some information or variable is removed from the set...

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Detalles Bibliográficos
Autores: Marín Mateos-Aparicio, José|||0000-0002-7825-2836, Mas Marí, José|||0000-0002-2835-974X, Guerrero-Flores, Danny Joel, Hayami, K.
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/105807
Acceso en línea:https://riunet.upv.es/handle/10251/105807
Access Level:acceso abierto
Palabra clave:Least squares problems
Iterative methods
Preconditioners
Low-rank updates
Sparse matrices
MATEMATICA APLICADA
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spelling Updating preconditioners for modified least squares problemsMarín Mateos-Aparicio, José|||0000-0002-7825-2836Mas Marí, José|||0000-0002-2835-974XGuerrero-Flores, Danny JoelHayami, K.Least squares problemsIterative methodsPreconditionersLow-rank updatesSparse matricesMATEMATICA APLICADA[EN] In this paper, we analyze how to update incomplete Cholesky preconditioners to solve least squares problems using iterative methods when the set of linear relations is updated with some new information, a new variable is added or, contrarily, some information or variable is removed from the set. Our proposed method computes a low-rank update of the preconditioner using a bordering method which is inexpensive compared with the cost of computing a new preconditioner. Moreover, the numerical experiments presented show that this strategy gives, in many cases, a better preconditioner than other choices, including the computation of a new preconditioner from scratch or reusing an existing one.Partially supported by Spanish Grants MTM2014-58159-P and MTM2015-68805-REDT.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería Agronómica y del Medio NaturalMinisterio de Economía y CompetitividadMinisterio de Economía, Industria y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/105807reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2015-68805-REDT RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONESMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICASopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1058072026-06-13T07:49:27Z
dc.title.none.fl_str_mv Updating preconditioners for modified least squares problems
title Updating preconditioners for modified least squares problems
spellingShingle Updating preconditioners for modified least squares problems
Marín Mateos-Aparicio, José|||0000-0002-7825-2836
Least squares problems
Iterative methods
Preconditioners
Low-rank updates
Sparse matrices
MATEMATICA APLICADA
title_short Updating preconditioners for modified least squares problems
title_full Updating preconditioners for modified least squares problems
title_fullStr Updating preconditioners for modified least squares problems
title_full_unstemmed Updating preconditioners for modified least squares problems
title_sort Updating preconditioners for modified least squares problems
dc.creator.none.fl_str_mv Marín Mateos-Aparicio, José|||0000-0002-7825-2836
Mas Marí, José|||0000-0002-2835-974X
Guerrero-Flores, Danny Joel
Hayami, K.
author Marín Mateos-Aparicio, José|||0000-0002-7825-2836
author_facet Marín Mateos-Aparicio, José|||0000-0002-7825-2836
Mas Marí, José|||0000-0002-2835-974X
Guerrero-Flores, Danny Joel
Hayami, K.
author_role author
author2 Mas Marí, José|||0000-0002-2835-974X
Guerrero-Flores, Danny Joel
Hayami, K.
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural
Ministerio de Economía y Competitividad
Ministerio de Economía, Industria y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Least squares problems
Iterative methods
Preconditioners
Low-rank updates
Sparse matrices
MATEMATICA APLICADA
topic Least squares problems
Iterative methods
Preconditioners
Low-rank updates
Sparse matrices
MATEMATICA APLICADA
description [EN] In this paper, we analyze how to update incomplete Cholesky preconditioners to solve least squares problems using iterative methods when the set of linear relations is updated with some new information, a new variable is added or, contrarily, some information or variable is removed from the set. Our proposed method computes a low-rank update of the preconditioner using a bordering method which is inexpensive compared with the cost of computing a new preconditioner. Moreover, the numerical experiments presented show that this strategy gives, in many cases, a better preconditioner than other choices, including the computation of a new preconditioner from scratch or reusing an existing one.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/105807
url https://riunet.upv.es/handle/10251/105807
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2015-68805-REDT RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONES
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICAS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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