Parallel bidiagonalization of a dense matrix

Detalhes bibliográficos
Autor(a) principal: Campos, Carlos
Data de Publicação: 2007
Outros Autores: Guerrero, David, Hernandez, Vicente, Ralha, Rui
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/8804
Resumo: A new stable method for the reduction of rectangular dense matrices to bidiagonal form has been proposed recently. This is a one-sided method since it can be entirely expressed in terms of operations with (full) columns of the matrix under transformation. The algorithm is well suited to parallel computing and, in order to make it even more attractive for distributed memory systems, we introduce a modification which halves the number of communication instances. In this paper we present such a modification. A block organization of the algorithm to use level~3 BLAS routines seems difficult and, at least for the moment, it relies upon level~2 BLAS routines. Nevertheless, we found that our sequential code is competitive with the LAPACK DGEBRD routine. We also compare the time taken by our parallel codes and the ScaLAPACK PDGEBRD routine. We investigated the best data distribution schemes for the different codes and we can state that our parallel codes are also competitive with the ScaLAPACK routine.
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spelling Parallel bidiagonalization of a dense matrixBidiagonal reductionParallel algorithmsScience & TechnologyA new stable method for the reduction of rectangular dense matrices to bidiagonal form has been proposed recently. This is a one-sided method since it can be entirely expressed in terms of operations with (full) columns of the matrix under transformation. The algorithm is well suited to parallel computing and, in order to make it even more attractive for distributed memory systems, we introduce a modification which halves the number of communication instances. In this paper we present such a modification. A block organization of the algorithm to use level~3 BLAS routines seems difficult and, at least for the moment, it relies upon level~2 BLAS routines. Nevertheless, we found that our sequential code is competitive with the LAPACK DGEBRD routine. We also compare the time taken by our parallel codes and the ScaLAPACK PDGEBRD routine. We investigated the best data distribution schemes for the different codes and we can state that our parallel codes are also competitive with the ScaLAPACK routine.Fundação para a Ciência e a Tecnologia (FCT) - programa POCI 2010.Society for Industrial and Applied Mathematics (SIAM)Universidade do MinhoCampos, CarlosGuerrero, DavidHernandez, VicenteRalha, Rui2007-072007-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/8804eng"SIAM Journal on Matrix Analysis and Applications." ISSN 0895-4798. 29:3 (Jul. 2007) 826-837.0895-479810.1137/05062809Xhttp://www.siam.org/journals/simax/29-3/62809.htmlinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:19:41Zoai:repositorium.sdum.uminho.pt:1822/8804Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:12:39.496812Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Parallel bidiagonalization of a dense matrix
title Parallel bidiagonalization of a dense matrix
spellingShingle Parallel bidiagonalization of a dense matrix
Campos, Carlos
Bidiagonal reduction
Parallel algorithms
Science & Technology
title_short Parallel bidiagonalization of a dense matrix
title_full Parallel bidiagonalization of a dense matrix
title_fullStr Parallel bidiagonalization of a dense matrix
title_full_unstemmed Parallel bidiagonalization of a dense matrix
title_sort Parallel bidiagonalization of a dense matrix
author Campos, Carlos
author_facet Campos, Carlos
Guerrero, David
Hernandez, Vicente
Ralha, Rui
author_role author
author2 Guerrero, David
Hernandez, Vicente
Ralha, Rui
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Campos, Carlos
Guerrero, David
Hernandez, Vicente
Ralha, Rui
dc.subject.por.fl_str_mv Bidiagonal reduction
Parallel algorithms
Science & Technology
topic Bidiagonal reduction
Parallel algorithms
Science & Technology
description A new stable method for the reduction of rectangular dense matrices to bidiagonal form has been proposed recently. This is a one-sided method since it can be entirely expressed in terms of operations with (full) columns of the matrix under transformation. The algorithm is well suited to parallel computing and, in order to make it even more attractive for distributed memory systems, we introduce a modification which halves the number of communication instances. In this paper we present such a modification. A block organization of the algorithm to use level~3 BLAS routines seems difficult and, at least for the moment, it relies upon level~2 BLAS routines. Nevertheless, we found that our sequential code is competitive with the LAPACK DGEBRD routine. We also compare the time taken by our parallel codes and the ScaLAPACK PDGEBRD routine. We investigated the best data distribution schemes for the different codes and we can state that our parallel codes are also competitive with the ScaLAPACK routine.
publishDate 2007
dc.date.none.fl_str_mv 2007-07
2007-07-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/8804
url http://hdl.handle.net/1822/8804
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "SIAM Journal on Matrix Analysis and Applications." ISSN 0895-4798. 29:3 (Jul. 2007) 826-837.
0895-4798
10.1137/05062809X
http://www.siam.org/journals/simax/29-3/62809.html
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics (SIAM)
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics (SIAM)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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