Minimization problems for certain structured matrices
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/37920 |
Resumo: | For given $Z,B\in \mathbb{ C}^{n\times k}$, the problem of finding $A\in \mathbb{C}^{n\times n}$, in some prescribed class ${\cal W}$, that minimizes $\|AZ-B\|$ (Frobenius norm) has been considered by different authors for distinct classes ${\cal W}$. Here, we study this minimization problem for two other classes which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. We also consider (as others have done for other classes ${\cal W}$) the problem of minimizing $\|A-\tilde{A}\|$ where $\tilde{A}$ is given and $A$ is a solution of the previous problem. The key idea of our contribution is the reduction of each one of the above minimization problems to two independent subproblems in orthogonal subspaces of $\mathbb{C}^{n\times n}$. This is possible due to the special structures under consideration. We have developed MATLAB codes and present the numerical results of some tests. |
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Minimization problems for certain structured matricesLeast-squares approximationCentralizer of JMoore- Penrose inverseAnticentralizer of JCiências Naturais::MatemáticasScience & TechnologyFor given $Z,B\in \mathbb{ C}^{n\times k}$, the problem of finding $A\in \mathbb{C}^{n\times n}$, in some prescribed class ${\cal W}$, that minimizes $\|AZ-B\|$ (Frobenius norm) has been considered by different authors for distinct classes ${\cal W}$. Here, we study this minimization problem for two other classes which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. We also consider (as others have done for other classes ${\cal W}$) the problem of minimizing $\|A-\tilde{A}\|$ where $\tilde{A}$ is given and $A$ is a solution of the previous problem. The key idea of our contribution is the reduction of each one of the above minimization problems to two independent subproblems in orthogonal subspaces of $\mathbb{C}^{n\times n}$. This is possible due to the special structures under consideration. We have developed MATLAB codes and present the numerical results of some tests.National Natural Science Foundation of China, no. 11371075.International Linear Algebra SocietyUniversidade do MinhoZhongyun LiuRalha, RuiZhang, YulinFerreira, Carla2015-102015-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/37920eng1081-381010.13001/1081-3810.3144http://repository.uwyo.edu/ela/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:RCAAP2023-07-21T12:45:43Zoai:repositorium.sdum.uminho.pt:1822/37920Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:43:37.344630Repositório 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 |
Minimization problems for certain structured matrices |
title |
Minimization problems for certain structured matrices |
spellingShingle |
Minimization problems for certain structured matrices Zhongyun Liu Least-squares approximation Centralizer of J Moore- Penrose inverse Anticentralizer of J Ciências Naturais::Matemáticas Science & Technology |
title_short |
Minimization problems for certain structured matrices |
title_full |
Minimization problems for certain structured matrices |
title_fullStr |
Minimization problems for certain structured matrices |
title_full_unstemmed |
Minimization problems for certain structured matrices |
title_sort |
Minimization problems for certain structured matrices |
author |
Zhongyun Liu |
author_facet |
Zhongyun Liu Ralha, Rui Zhang, Yulin Ferreira, Carla |
author_role |
author |
author2 |
Ralha, Rui Zhang, Yulin Ferreira, Carla |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Zhongyun Liu Ralha, Rui Zhang, Yulin Ferreira, Carla |
dc.subject.por.fl_str_mv |
Least-squares approximation Centralizer of J Moore- Penrose inverse Anticentralizer of J Ciências Naturais::Matemáticas Science & Technology |
topic |
Least-squares approximation Centralizer of J Moore- Penrose inverse Anticentralizer of J Ciências Naturais::Matemáticas Science & Technology |
description |
For given $Z,B\in \mathbb{ C}^{n\times k}$, the problem of finding $A\in \mathbb{C}^{n\times n}$, in some prescribed class ${\cal W}$, that minimizes $\|AZ-B\|$ (Frobenius norm) has been considered by different authors for distinct classes ${\cal W}$. Here, we study this minimization problem for two other classes which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. We also consider (as others have done for other classes ${\cal W}$) the problem of minimizing $\|A-\tilde{A}\|$ where $\tilde{A}$ is given and $A$ is a solution of the previous problem. The key idea of our contribution is the reduction of each one of the above minimization problems to two independent subproblems in orthogonal subspaces of $\mathbb{C}^{n\times n}$. This is possible due to the special structures under consideration. We have developed MATLAB codes and present the numerical results of some tests. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-10 2015-10-01T00:00:00Z |
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/1822/37920 |
url |
http://hdl.handle.net/1822/37920 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1081-3810 10.13001/1081-3810.3144 http://repository.uwyo.edu/ela/ |
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 |
repository.mail.fl_str_mv |
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1799132994324135936 |