Eigenpairs of Wilkinson Matrices
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/69416 |
Resumo: | In the 1950s J. H. Wilkinson introduced two families of symmetric tridiagonal integer matrices. Most of the eigenvalues are close to diagonal entries. We develop the structure of their eigenvectors in a natural way which reveals that these eigenvectors all look the same to the naked eye. The shape of the envelopes is like twin peaks (or a badly dented bell curve). We also analyze the eigenvectors of the remaining noninteger eigenvalues. |
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Eigenpairs of Wilkinson MatricesWilkinson matrixEigensystemPersymmetryCiências Naturais::MatemáticasScience & TechnologyIn the 1950s J. H. Wilkinson introduced two families of symmetric tridiagonal integer matrices. Most of the eigenvalues are close to diagonal entries. We develop the structure of their eigenvectors in a natural way which reveals that these eigenvectors all look the same to the naked eye. The shape of the envelopes is like twin peaks (or a badly dented bell curve). We also analyze the eigenvectors of the remaining noninteger eigenvalues.FCT -Fundação para a Ciência e a Tecnologia(UID/MAT/00013/2013)Society for Industrial and Applied Mathematics (SIAM)Universidade do MinhoFerreira, CarlaParlett, Beresford2020-09-212020-09-21T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/69416eng0895-47981095-716210.1137/20M1327343https://doi.org/10.1137/20M1327343info: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:RCAAP2023-07-21T12:14:16Zoai:repositorium.sdum.uminho.pt:1822/69416Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:06:34.155910Repositório 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 |
Eigenpairs of Wilkinson Matrices |
title |
Eigenpairs of Wilkinson Matrices |
spellingShingle |
Eigenpairs of Wilkinson Matrices Ferreira, Carla Wilkinson matrix Eigensystem Persymmetry Ciências Naturais::Matemáticas Science & Technology |
title_short |
Eigenpairs of Wilkinson Matrices |
title_full |
Eigenpairs of Wilkinson Matrices |
title_fullStr |
Eigenpairs of Wilkinson Matrices |
title_full_unstemmed |
Eigenpairs of Wilkinson Matrices |
title_sort |
Eigenpairs of Wilkinson Matrices |
author |
Ferreira, Carla |
author_facet |
Ferreira, Carla Parlett, Beresford |
author_role |
author |
author2 |
Parlett, Beresford |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Ferreira, Carla Parlett, Beresford |
dc.subject.por.fl_str_mv |
Wilkinson matrix Eigensystem Persymmetry Ciências Naturais::Matemáticas Science & Technology |
topic |
Wilkinson matrix Eigensystem Persymmetry Ciências Naturais::Matemáticas Science & Technology |
description |
In the 1950s J. H. Wilkinson introduced two families of symmetric tridiagonal integer matrices. Most of the eigenvalues are close to diagonal entries. We develop the structure of their eigenvectors in a natural way which reveals that these eigenvectors all look the same to the naked eye. The shape of the envelopes is like twin peaks (or a badly dented bell curve). We also analyze the eigenvectors of the remaining noninteger eigenvalues. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-09-21 2020-09-21T00:00:00Z |
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/1822/69416 |
url |
http://hdl.handle.net/1822/69416 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0895-4798 1095-7162 10.1137/20M1327343 https://doi.org/10.1137/20M1327343 |
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 |
Society for Industrial and Applied Mathematics (SIAM) |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics (SIAM) |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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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 |
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1799132481580957696 |