Positive bidiagonal factorization of tetradiagonal Hessenberg matrices

Detalhes bibliográficos
Autor(a) principal: Branquinho, Amílcar
Data de Publicação: 2023
Outros Autores: Foulquié-Moreno, Ana, Mañas, Manuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10773/39325
Resumo: Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal Hessenberg matrix can have such a positive bidiagonal factorization. Oscillatory tetradiagonal Toeplitz matrices are examined as a case study of matrices that admit a positive bidiagonal factorization. Furthermore, the paper proves that oscillatory banded Hessenberg matrices are organized in rays, where the origin of the ray does not have a positive bidiagonal factorization, but all the interior points of the ray do have such a positive bidiagonal factorization.
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spelling Positive bidiagonal factorization of tetradiagonal Hessenberg matricesBanded Hessenberg matricesOscillatory matricesTotally nonnegative matricesContinued fractionsGauss–Borel factorizationBidiagonal factorizationOscillatory retracted matricesRecently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal Hessenberg matrix can have such a positive bidiagonal factorization. Oscillatory tetradiagonal Toeplitz matrices are examined as a case study of matrices that admit a positive bidiagonal factorization. Furthermore, the paper proves that oscillatory banded Hessenberg matrices are organized in rays, where the origin of the ray does not have a positive bidiagonal factorization, but all the interior points of the ray do have such a positive bidiagonal factorization.Elsevier2023-09-06T17:03:35Z2023-11-15T00:00:00Z2023-11-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39325eng0024-379510.1016/j.laa.2023.08.001Branquinho, AmílcarFoulquié-Moreno, AnaMañas, Manuelinfo: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:RCAAP2024-05-06T04:49:18Zoai:ria.ua.pt:10773/39325Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:21:27.266356Repositórios 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 Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
title Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
spellingShingle Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
Branquinho, Amílcar
Banded Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Continued fractions
Gauss–Borel factorization
Bidiagonal factorization
Oscillatory retracted matrices
title_short Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
title_full Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
title_fullStr Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
title_full_unstemmed Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
title_sort Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
author Branquinho, Amílcar
author_facet Branquinho, Amílcar
Foulquié-Moreno, Ana
Mañas, Manuel
author_role author
author2 Foulquié-Moreno, Ana
Mañas, Manuel
author2_role author
author
dc.contributor.author.fl_str_mv Branquinho, Amílcar
Foulquié-Moreno, Ana
Mañas, Manuel
dc.subject.por.fl_str_mv Banded Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Continued fractions
Gauss–Borel factorization
Bidiagonal factorization
Oscillatory retracted matrices
topic Banded Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Continued fractions
Gauss–Borel factorization
Bidiagonal factorization
Oscillatory retracted matrices
description Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal Hessenberg matrix can have such a positive bidiagonal factorization. Oscillatory tetradiagonal Toeplitz matrices are examined as a case study of matrices that admit a positive bidiagonal factorization. Furthermore, the paper proves that oscillatory banded Hessenberg matrices are organized in rays, where the origin of the ray does not have a positive bidiagonal factorization, but all the interior points of the ray do have such a positive bidiagonal factorization.
publishDate 2023
dc.date.none.fl_str_mv 2023-09-06T17:03:35Z
2023-11-15T00:00:00Z
2023-11-15
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/10773/39325
url http://hdl.handle.net/10773/39325
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
10.1016/j.laa.2023.08.001
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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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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