A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation

[EN] Large-scale polynomial eigenvalue problems can be solved by Krylov methods operating on an equivalent linear eigenproblem (linearization) of size d center dot n where d is the polynomial degree and n is the problem size, or by projection methods that keep the computation in the n-dimensional sp...

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Detalhes bibliográficos
Autores: Campos, Carmen, Jose E. Roman|||0000-0003-1144-6772
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/161207
Acesso em linha:https://riunet.upv.es/handle/10251/161207
Access Level:acceso abierto
Palavra-chave:Polynomial eigenvalue problem
Jacobi-Davidson
Non-monomial bases
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
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spelling A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflationCampos, CarmenJose E. Roman|||0000-0003-1144-6772Polynomial eigenvalue problemJacobi-DavidsonNon-monomial basesSLEPcCIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL[EN] Large-scale polynomial eigenvalue problems can be solved by Krylov methods operating on an equivalent linear eigenproblem (linearization) of size d center dot n where d is the polynomial degree and n is the problem size, or by projection methods that keep the computation in the n-dimensional space. Jacobi-Davidson belongs to the latter class of methods, and, since it is a preconditioned eigensolver, it may be competitive in cases where explicitly computing a matrix factorization is exceedingly expensive. However, a fully fledged implementation of polynomial Jacobi-Davidson has to consider several issues, including deflation to compute more than one eigenpair, use of non-monomial bases for the case of large degree polynomials, and handling of complex eigenvalues when computing in real arithmetic. We discuss these aspects and present computational results of a parallel implementation in the SLEPc library.This work was supported by Agencia Estatal de Investigación (AEI) under Grant TIN2016-75985-P, which includes European Commission ERDF funds.Springer-VerlagDepartamento de Sistemas Informáticos y ComputaciónEscuela Técnica Superior de Ingeniería InformáticaAgencia Estatal de InvestigaciónEuropean Regional Development FundMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/161207reponame: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 TIN2016-75985-P SOLVERS DE VALORES PROPIOS ALTAMENTE ESCALABLES EN EL CONTEXTO DE LA BIBLIOTECA SLEPCAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-107379RB-I00 ALGORITMOS PARALELOS Y SOFTWARE PARA METODOS ALGEBRAICOS EN ANALISIS DE DATOSopen 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:10251/1612072026-06-13T07:49:27Z
dc.title.none.fl_str_mv A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
title A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
spellingShingle A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
Campos, Carmen
Polynomial eigenvalue problem
Jacobi-Davidson
Non-monomial bases
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
title_short A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
title_full A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
title_fullStr A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
title_full_unstemmed A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
title_sort A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation
dc.creator.none.fl_str_mv Campos, Carmen
Jose E. Roman|||0000-0003-1144-6772
author Campos, Carmen
author_facet Campos, Carmen
Jose E. Roman|||0000-0003-1144-6772
author_role author
author2 Jose E. Roman|||0000-0003-1144-6772
author2_role author
dc.contributor.none.fl_str_mv Departamento de Sistemas Informáticos y Computación
Escuela Técnica Superior de Ingeniería Informática
Agencia Estatal de Investigación
European Regional Development Fund
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Polynomial eigenvalue problem
Jacobi-Davidson
Non-monomial bases
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
topic Polynomial eigenvalue problem
Jacobi-Davidson
Non-monomial bases
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
description [EN] Large-scale polynomial eigenvalue problems can be solved by Krylov methods operating on an equivalent linear eigenproblem (linearization) of size d center dot n where d is the polynomial degree and n is the problem size, or by projection methods that keep the computation in the n-dimensional space. Jacobi-Davidson belongs to the latter class of methods, and, since it is a preconditioned eigensolver, it may be competitive in cases where explicitly computing a matrix factorization is exceedingly expensive. However, a fully fledged implementation of polynomial Jacobi-Davidson has to consider several issues, including deflation to compute more than one eigenpair, use of non-monomial bases for the case of large degree polynomials, and handling of complex eigenvalues when computing in real arithmetic. We discuss these aspects and present computational results of a parallel implementation in the SLEPc library.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-06-01
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/10251/161207
url https://riunet.upv.es/handle/10251/161207
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 TIN2016-75985-P SOLVERS DE VALORES PROPIOS ALTAMENTE ESCALABLES EN EL CONTEXTO DE LA BIBLIOTECA SLEPC
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-107379RB-I00 ALGORITMOS PARALELOS Y SOFTWARE PARA METODOS ALGEBRAICOS EN ANALISIS DE DATOS
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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