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The inverse eigenvector problem for real tridiagonal matrices

Bibliographic Details
Main Author: Parlett, Beresford
Publication Date: 2016
Other Authors: Dopico, Froilán M., Ferreira, Carla
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/1822/47617
Summary: 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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spelling 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-11T07:35:18Zoai:repositorium.sdum.uminho.pt:1822/47617Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T16:32:35.416563Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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