On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks

Detalhes bibliográficos
Autor(a) principal: Zhang Yulin
Data de Publicação: 2010
Outros Autores: Liu Zhongyun, Ferreira, Carla, Ralha, Rui
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/11391
Resumo: We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.
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spelling On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocksBlock Toeplitz matrixNewton methodInverse eigenvalue problemGeneralized K-centrosymmetric matrixScience & TechnologyWe propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.Fundação para a Ciência e a Tecnologia (FCT)ElsevierUniversidade do MinhoZhang YulinLiu ZhongyunFerreira, CarlaRalha, Rui20102010-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/11391eng"Applied Mathematics and Computation". ISSN 0096-3003. 216 (2010) 1819-1830.0096-300310.1016/j.amc.2009.12.023www.elsevier.cominfo: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:RCAAP2023-07-21T12:23:24Zoai:repositorium.sdum.uminho.pt:1822/11391Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:17:06.326108Repositório 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 On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
title On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
spellingShingle On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
Zhang Yulin
Block Toeplitz matrix
Newton method
Inverse eigenvalue problem
Generalized K-centrosymmetric matrix
Science & Technology
title_short On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
title_full On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
title_fullStr On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
title_full_unstemmed On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
title_sort On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
author Zhang Yulin
author_facet Zhang Yulin
Liu Zhongyun
Ferreira, Carla
Ralha, Rui
author_role author
author2 Liu Zhongyun
Ferreira, Carla
Ralha, Rui
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Zhang Yulin
Liu Zhongyun
Ferreira, Carla
Ralha, Rui
dc.subject.por.fl_str_mv Block Toeplitz matrix
Newton method
Inverse eigenvalue problem
Generalized K-centrosymmetric matrix
Science & Technology
topic Block Toeplitz matrix
Newton method
Inverse eigenvalue problem
Generalized K-centrosymmetric matrix
Science & Technology
description We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01T00:00:00Z
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/1822/11391
url http://hdl.handle.net/1822/11391
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Applied Mathematics and Computation". ISSN 0096-3003. 216 (2010) 1819-1830.
0096-3003
10.1016/j.amc.2009.12.023
www.elsevier.com
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: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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