An iterative method for solving a kind of constrained linear matrix equations system

Detalhes bibliográficos
Autor(a) principal: Cai,Jing
Data de Publicação: 2009
Outros Autores: Chen,Guoliang
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004
Resumo: In this paper, an iterative method is constructed to solve the following constrained linear matrix equations system: [A1(X),A2(X),... ,Ar(X)]=[E1,E2, ... ,Er ], X ∈ I={X |X= U(X)}, where Ai is a linear operator from Cmxn onto Cpixqi, Ei ∈ Cpixqi, i=1 , 2,..., r , and U is a linear self-conjugate involution operator. When the above constrained matrix equations system is consistent, for any initial matrix X0 ∈ I, a solution can be obtained by the proposed iterative method in finite iteration steps in the absence of roundoff errors, and the least Frobenius norm solution can be derived when a special kind of initial matrix is chosen. Furthermore, the optimal approximation solution to a given matrix can be derived. Several numerical examples are given to show the efficiency of the presented iterative method. Mathematical subject classification: 15A24, 65D99,65F30.
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spelling An iterative method for solving a kind of constrained linear matrix equations systemiterative methodlinear matrix equations systemlinear operatorleast Frobenius norm solutionoptimal approximationIn this paper, an iterative method is constructed to solve the following constrained linear matrix equations system: [A1(X),A2(X),... ,Ar(X)]=[E1,E2, ... ,Er ], X ∈ I={X |X= U(X)}, where Ai is a linear operator from Cmxn onto Cpixqi, Ei ∈ Cpixqi, i=1 , 2,..., r , and U is a linear self-conjugate involution operator. When the above constrained matrix equations system is consistent, for any initial matrix X0 ∈ I, a solution can be obtained by the proposed iterative method in finite iteration steps in the absence of roundoff errors, and the least Frobenius norm solution can be derived when a special kind of initial matrix is chosen. Furthermore, the optimal approximation solution to a given matrix can be derived. Several numerical examples are given to show the efficiency of the presented iterative method. Mathematical subject classification: 15A24, 65D99,65F30.Sociedade Brasileira de Matemática Aplicada e Computacional2009-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004Computational & Applied Mathematics v.28 n.3 2009reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022009000300004info:eu-repo/semantics/openAccessCai,JingChen,Guoliangeng2009-11-05T00:00:00Zoai:scielo:S1807-03022009000300004Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2009-11-05T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv An iterative method for solving a kind of constrained linear matrix equations system
title An iterative method for solving a kind of constrained linear matrix equations system
spellingShingle An iterative method for solving a kind of constrained linear matrix equations system
Cai,Jing
iterative method
linear matrix equations system
linear operator
least Frobenius norm solution
optimal approximation
title_short An iterative method for solving a kind of constrained linear matrix equations system
title_full An iterative method for solving a kind of constrained linear matrix equations system
title_fullStr An iterative method for solving a kind of constrained linear matrix equations system
title_full_unstemmed An iterative method for solving a kind of constrained linear matrix equations system
title_sort An iterative method for solving a kind of constrained linear matrix equations system
author Cai,Jing
author_facet Cai,Jing
Chen,Guoliang
author_role author
author2 Chen,Guoliang
author2_role author
dc.contributor.author.fl_str_mv Cai,Jing
Chen,Guoliang
dc.subject.por.fl_str_mv iterative method
linear matrix equations system
linear operator
least Frobenius norm solution
optimal approximation
topic iterative method
linear matrix equations system
linear operator
least Frobenius norm solution
optimal approximation
description In this paper, an iterative method is constructed to solve the following constrained linear matrix equations system: [A1(X),A2(X),... ,Ar(X)]=[E1,E2, ... ,Er ], X ∈ I={X |X= U(X)}, where Ai is a linear operator from Cmxn onto Cpixqi, Ei ∈ Cpixqi, i=1 , 2,..., r , and U is a linear self-conjugate involution operator. When the above constrained matrix equations system is consistent, for any initial matrix X0 ∈ I, a solution can be obtained by the proposed iterative method in finite iteration steps in the absence of roundoff errors, and the least Frobenius norm solution can be derived when a special kind of initial matrix is chosen. Furthermore, the optimal approximation solution to a given matrix can be derived. Several numerical examples are given to show the efficiency of the presented iterative method. Mathematical subject classification: 15A24, 65D99,65F30.
publishDate 2009
dc.date.none.fl_str_mv 2009-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022009000300004
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.28 n.3 2009
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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