An iterative method for solving a kind of constrained linear matrix equations system
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
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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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 |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004 |
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 |
_version_ |
1754734890194042880 |