Theoretical and numerical considerations about Padé approximants for the matrix logarithm

Detalhes bibliográficos
Autor(a) principal: Cardoso, J. R.
Data de Publicação: 2001
Outros Autores: Silva Leite, F.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4648
https://doi.org/10.1016/S0024-3795(01)00251-8
Resumo: We show that for a vast class of matrix Lie groups, which includes the orthogonal and the symplectic, diagonal Padé approximants of log((1+x)/(1-x)) are structure preserving. The conditioning of these approximants is analyzed. We also present a new algorithm for the Briggs-Padé method, based on a strategy for reducing the number of square roots in the inverse scaling and squaring procedure.
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spelling Theoretical and numerical considerations about Padé approximants for the matrix logarithmP-orthogonal groupsMatrix logarithmsPadé approximantsCondition numberWe show that for a vast class of matrix Lie groups, which includes the orthogonal and the symplectic, diagonal Padé approximants of log((1+x)/(1-x)) are structure preserving. The conditioning of these approximants is analyzed. We also present a new algorithm for the Briggs-Padé method, based on a strategy for reducing the number of square roots in the inverse scaling and squaring procedure.http://www.sciencedirect.com/science/article/B6V0R-439WFRV-4/1/a3695a33e70aef2dd31f867ef9c1c8fc2001info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4648http://hdl.handle.net/10316/4648https://doi.org/10.1016/S0024-3795(01)00251-8engLinear Algebra and its Applications. 330:1-3 (2001) 31-42Cardoso, J. R.Silva Leite, F.info: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:RCAAP2020-11-06T16:59:33Zoai:estudogeral.uc.pt:10316/4648Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:40.785874Repositório 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 Theoretical and numerical considerations about Padé approximants for the matrix logarithm
title Theoretical and numerical considerations about Padé approximants for the matrix logarithm
spellingShingle Theoretical and numerical considerations about Padé approximants for the matrix logarithm
Cardoso, J. R.
P-orthogonal groups
Matrix logarithms
Padé approximants
Condition number
title_short Theoretical and numerical considerations about Padé approximants for the matrix logarithm
title_full Theoretical and numerical considerations about Padé approximants for the matrix logarithm
title_fullStr Theoretical and numerical considerations about Padé approximants for the matrix logarithm
title_full_unstemmed Theoretical and numerical considerations about Padé approximants for the matrix logarithm
title_sort Theoretical and numerical considerations about Padé approximants for the matrix logarithm
author Cardoso, J. R.
author_facet Cardoso, J. R.
Silva Leite, F.
author_role author
author2 Silva Leite, F.
author2_role author
dc.contributor.author.fl_str_mv Cardoso, J. R.
Silva Leite, F.
dc.subject.por.fl_str_mv P-orthogonal groups
Matrix logarithms
Padé approximants
Condition number
topic P-orthogonal groups
Matrix logarithms
Padé approximants
Condition number
description We show that for a vast class of matrix Lie groups, which includes the orthogonal and the symplectic, diagonal Padé approximants of log((1+x)/(1-x)) are structure preserving. The conditioning of these approximants is analyzed. We also present a new algorithm for the Briggs-Padé method, based on a strategy for reducing the number of square roots in the inverse scaling and squaring procedure.
publishDate 2001
dc.date.none.fl_str_mv 2001
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/10316/4648
http://hdl.handle.net/10316/4648
https://doi.org/10.1016/S0024-3795(01)00251-8
url http://hdl.handle.net/10316/4648
https://doi.org/10.1016/S0024-3795(01)00251-8
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Linear Algebra and its Applications. 330:1-3 (2001) 31-42
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv aplication/PDF
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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