The geometric mean algorithm

Detalhes bibliográficos
Autor(a) principal: Ralha, Rui
Data de Publicação: 2012
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/20483
Resumo: Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a,b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometric bisection in a Matlab code. We illustrate the effectiveness of our algorithm in the context of the computation of the eigenvalues of a symmetric tridiagonal matrix which has a very large condition number.
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spelling The geometric mean algorithmEigenvaluesSymmetric matricesGeometric bisectionScience & TechnologyBisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a,b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometric bisection in a Matlab code. We illustrate the effectiveness of our algorithm in the context of the computation of the eigenvalues of a symmetric tridiagonal matrix which has a very large condition number.Fundação para a Ciência e a Tecnologia (FCT)ElsevierUniversidade do MinhoRalha, Rui2012-112012-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/20483eng0096-300310.1016/j.amc.2012.08.002info: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:RCAAP2023-07-21T12:27:18Zoai:repositorium.sdum.uminho.pt:1822/20483Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:21:51.972213Repositório 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 The geometric mean algorithm
title The geometric mean algorithm
spellingShingle The geometric mean algorithm
Ralha, Rui
Eigenvalues
Symmetric matrices
Geometric bisection
Science & Technology
title_short The geometric mean algorithm
title_full The geometric mean algorithm
title_fullStr The geometric mean algorithm
title_full_unstemmed The geometric mean algorithm
title_sort The geometric mean algorithm
author Ralha, Rui
author_facet Ralha, Rui
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Ralha, Rui
dc.subject.por.fl_str_mv Eigenvalues
Symmetric matrices
Geometric bisection
Science & Technology
topic Eigenvalues
Symmetric matrices
Geometric bisection
Science & Technology
description Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a,b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometric bisection in a Matlab code. We illustrate the effectiveness of our algorithm in the context of the computation of the eigenvalues of a symmetric tridiagonal matrix which has a very large condition number.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
2012-11-01T00:00:00Z
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/1822/20483
url http://hdl.handle.net/1822/20483
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0096-3003
10.1016/j.amc.2012.08.002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
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