The geometric mean algorithm
Autor(a) principal: | |
---|---|
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. |
id |
RCAP_cfa270ed5451abdb17325fd18b112788 |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/20483 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 |
institution |
RCAAP |
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 |
|
_version_ |
1799132686672986112 |