Bidiagonal factorization of tetradiagonal matrices and Darboux transformations

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: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/38123
Resumo: Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin.
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spelling Bidiagonal factorization of tetradiagonal matrices and Darboux transformationsTetradiagonal Hessenberg matricesOscillatory matricesTotally nonnegative matricesMultiple orthogonal polynomialsFavard spectral representationDarboux transformationsChristofel FormulasRecently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin.Springer2023-06-19T09:39:14Z2023-04-16T00:00:00Z2023-04-16info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/38123eng1664-236810.1007/s13324-023-00801-1Branquinho, AmílcarFoulquié-Moreno, AnaMañas, Manuelinfo: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:RCAAP2024-02-22T12:14:26Zoai:ria.ua.pt:10773/38123Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:08:39.455821Repositório 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 Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
title Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
spellingShingle Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
Branquinho, Amílcar
Tetradiagonal Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Multiple orthogonal polynomials
Favard spectral representation
Darboux transformations
Christofel Formulas
title_short Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
title_full Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
title_fullStr Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
title_full_unstemmed Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
title_sort Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
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 Tetradiagonal Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Multiple orthogonal polynomials
Favard spectral representation
Darboux transformations
Christofel Formulas
topic Tetradiagonal Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Multiple orthogonal polynomials
Favard spectral representation
Darboux transformations
Christofel Formulas
description Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin.
publishDate 2023
dc.date.none.fl_str_mv 2023-06-19T09:39:14Z
2023-04-16T00:00:00Z
2023-04-16
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/10773/38123
url http://hdl.handle.net/10773/38123
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1664-2368
10.1007/s13324-023-00801-1
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 Springer
publisher.none.fl_str_mv Springer
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
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