Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc

Polynomial eigenvalue problems are often found in scientific computing applications. When the coefficient matrices of the polynomial are large and sparse, usually only a few eigenpairs are required and projection methods are the best choice. We focus on Krylov methods that operate on the companion l...

ver descrição completa

Detalhes bibliográficos
Autores: Campos, Carmen, Jose E. Roman|||0000-0003-1144-6772
Formato: artículo
Fecha de publicación:2016
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:10251/80768
Acesso em linha:https://riunet.upv.es/handle/10251/80768
Access Level:acceso abierto
Palavra-chave:Matrix polynomial
Eigenvalues
Companion linearization
Krylov subspace
Nonmonomial bases
Spectral transformation
Parallel computing
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
id ES_2e4b7d334f92c8ece5d875b3ae947537
oai_identifier_str oai:riunet.upv.es:10251/80768
network_acronym_str ES
network_name_str España
repository_id_str
spelling Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPcCampos, CarmenJose E. Roman|||0000-0003-1144-6772Matrix polynomialEigenvaluesCompanion linearizationKrylov subspaceNonmonomial basesSpectral transformationParallel computingSLEPcCIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIALPolynomial eigenvalue problems are often found in scientific computing applications. When the coefficient matrices of the polynomial are large and sparse, usually only a few eigenpairs are required and projection methods are the best choice. We focus on Krylov methods that operate on the companion linearization of the polynomial but exploit the block structure with the aim of being memory-efficient in the representation of the Krylov subspace basis. The problem may appear in the form of a low-degree polynomial (quartic or quintic, say) expressed in the monomial basis, or a high-degree polynomial (coming from interpolation of a nonlinear eigenproblem) expressed in a nonmonomial basis. We have implemented a parallel solver in SLEPc covering both cases that is able to compute exterior as well as interior eigenvalues via spectral transformation. We discuss important issues such as scaling and restart and illustrate the robustness and performance of the solver with some numerical experiments.The first author was supported by the Spanish Ministry of Education, Culture and Sport through an FPU grant with reference AP2012-0608.Society for Industrial and Applied MathematicsDepartamento de Sistemas Informáticos y ComputaciónEscuela Técnica Superior de Ingeniería InformáticaMinisterio de Educación, Cultura y DeporteMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20162016-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/80768reponame: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 TIN2013-41049-P EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTESMinisterio de Educación y Cultura http://dx.doi.org/10.13039/501100003176 AP2012-0608 AP2012-0608open 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:10251/807682026-06-13T07:49:27Z
dc.title.none.fl_str_mv Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
title Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
spellingShingle Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
Campos, Carmen
Matrix polynomial
Eigenvalues
Companion linearization
Krylov subspace
Nonmonomial bases
Spectral transformation
Parallel computing
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
title_short Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
title_full Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
title_fullStr Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
title_full_unstemmed Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
title_sort Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
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
Ministerio de Educación, Cultura y Deporte
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix polynomial
Eigenvalues
Companion linearization
Krylov subspace
Nonmonomial bases
Spectral transformation
Parallel computing
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
topic Matrix polynomial
Eigenvalues
Companion linearization
Krylov subspace
Nonmonomial bases
Spectral transformation
Parallel computing
SLEPc
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
description Polynomial eigenvalue problems are often found in scientific computing applications. When the coefficient matrices of the polynomial are large and sparse, usually only a few eigenpairs are required and projection methods are the best choice. We focus on Krylov methods that operate on the companion linearization of the polynomial but exploit the block structure with the aim of being memory-efficient in the representation of the Krylov subspace basis. The problem may appear in the form of a low-degree polynomial (quartic or quintic, say) expressed in the monomial basis, or a high-degree polynomial (coming from interpolation of a nonlinear eigenproblem) expressed in a nonmonomial basis. We have implemented a parallel solver in SLEPc covering both cases that is able to compute exterior as well as interior eigenvalues via spectral transformation. We discuss important issues such as scaling and restart and illustrate the robustness and performance of the solver with some numerical experiments.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
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/10251/80768
url https://riunet.upv.es/handle/10251/80768
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 TIN2013-41049-P EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTES
Ministerio de Educación y Cultura http://dx.doi.org/10.13039/501100003176 AP2012-0608 AP2012-0608
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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
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
_version_ 1869405394404638720
score 15.228081

Registos relacionados