The inverse eigenvector problem for real tridiagonal matrices
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/1822/47617 |
Resumo: | A little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors is exact. Similarly, we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with different real eigenvalues, are also exact. We close with an illustration that these unique “backward error” matrices are sensitive to small rounding errors in certain partial sums which play a key role in determining the matrices. |
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The inverse eigenvector problem for real tridiagonal matricesBackward errorsTridiagonal matricesEigenvectorCiências Naturais::MatemáticasScience & TechnologyA little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors is exact. Similarly, we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with different real eigenvalues, are also exact. We close with an illustration that these unique “backward error” matrices are sensitive to small rounding errors in certain partial sums which play a key role in determining the matrices.Ministerio de Economía y Competitividad of Spain through research grant MTM2012-32542info:eu-repo/semantics/publishedVersionSociety for Industrial and Applied MathematicsUniversidade do MinhoParlett, BeresfordDopico, Froilán M.Ferreira, Carla2016-04-272016-04-27T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/47617eng0895-479810.1137/15M1025293http://epubs.siam.org/doi/abs/10.1137/15M1025293info: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:RCAAP2023-07-21T12:53:04Zoai:repositorium.sdum.uminho.pt:1822/47617Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:52:21.289553Repositório 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 inverse eigenvector problem for real tridiagonal matrices |
title |
The inverse eigenvector problem for real tridiagonal matrices |
spellingShingle |
The inverse eigenvector problem for real tridiagonal matrices Parlett, Beresford Backward errors Tridiagonal matrices Eigenvector Ciências Naturais::Matemáticas Science & Technology |
title_short |
The inverse eigenvector problem for real tridiagonal matrices |
title_full |
The inverse eigenvector problem for real tridiagonal matrices |
title_fullStr |
The inverse eigenvector problem for real tridiagonal matrices |
title_full_unstemmed |
The inverse eigenvector problem for real tridiagonal matrices |
title_sort |
The inverse eigenvector problem for real tridiagonal matrices |
author |
Parlett, Beresford |
author_facet |
Parlett, Beresford Dopico, Froilán M. Ferreira, Carla |
author_role |
author |
author2 |
Dopico, Froilán M. Ferreira, Carla |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Parlett, Beresford Dopico, Froilán M. Ferreira, Carla |
dc.subject.por.fl_str_mv |
Backward errors Tridiagonal matrices Eigenvector Ciências Naturais::Matemáticas Science & Technology |
topic |
Backward errors Tridiagonal matrices Eigenvector Ciências Naturais::Matemáticas Science & Technology |
description |
A little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors is exact. Similarly, we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with different real eigenvalues, are also exact. We close with an illustration that these unique “backward error” matrices are sensitive to small rounding errors in certain partial sums which play a key role in determining the matrices. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-04-27 2016-04-27T00:00:00Z |
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/1822/47617 |
url |
http://hdl.handle.net/1822/47617 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0895-4798 10.1137/15M1025293 http://epubs.siam.org/doi/abs/10.1137/15M1025293 |
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 |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
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 |
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1799133115574124544 |