Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices

Detalhes bibliográficos
Autor(a) principal: Liu Zhongyun
Data de Publicação: 2012
Outros Autores: Zhang Yulin, 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/1822/20735
Resumo: The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic.
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spelling Structure-preserving schur methods for computing square roots of real skew-hamiltonian matricesMatrix square rootSkew-Hamiltonian Schur decompositionStructure-preserving algorithmScience & TechnologyThe contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic.National Natural Science Foundations of China, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry,Fundação para a Ciência e a Tecnologia (FCT)International Linear Algebra SocietyUniversidade do MinhoLiu ZhongyunZhang YulinFerreira, CarlaRalha, Rui2012-092012-09-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/20735eng1081-3810http://www.math.technion.ac.il/info: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:RCAAP2023-07-21T12:19:29Zoai:repositorium.sdum.uminho.pt:1822/20735Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:12:25.524340Repositório 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 Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
title Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
spellingShingle Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
Liu Zhongyun
Matrix square root
Skew-Hamiltonian Schur decomposition
Structure-preserving algorithm
Science & Technology
title_short Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
title_full Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
title_fullStr Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
title_full_unstemmed Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
title_sort Structure-preserving schur methods for computing square roots of real skew-hamiltonian matrices
author Liu Zhongyun
author_facet Liu Zhongyun
Zhang Yulin
Ferreira, Carla
Ralha, Rui
author_role author
author2 Zhang Yulin
Ferreira, Carla
Ralha, Rui
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Liu Zhongyun
Zhang Yulin
Ferreira, Carla
Ralha, Rui
dc.subject.por.fl_str_mv Matrix square root
Skew-Hamiltonian Schur decomposition
Structure-preserving algorithm
Science & Technology
topic Matrix square root
Skew-Hamiltonian Schur decomposition
Structure-preserving algorithm
Science & Technology
description The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic.
publishDate 2012
dc.date.none.fl_str_mv 2012-09
2012-09-01T00:00:00Z
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/1822/20735
url http://hdl.handle.net/1822/20735
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1081-3810
http://www.math.technion.ac.il/
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 International Linear Algebra Society
publisher.none.fl_str_mv International Linear Algebra Society
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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