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

Bibliographic Details
Main Author: Liu Zhongyun
Publication Date: 2012
Other Authors: Zhang Yulin, Ferreira, Carla, Ralha, Rui
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/1822/20735
Summary: 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-11T05:38:23Zoai:repositorium.sdum.uminho.pt:1822/20735Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:25:00.052937Repositórios 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 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: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
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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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