An iterative method for solving a kind of constrained linear matrix equations system
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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Sociedade Brasileira de Matemática Aplicada e Computacional
2009
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oai:scielo:S1807-030220090003000042009-11-05An iterative method for solving a kind of constrained linear matrix equations systemCai,JingChen,Guoliang iterative method linear matrix equations system linear operator least Frobenius norm solution optimal approximation 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.info:eu-repo/semantics/openAccessSociedade Brasileira de Matemática Aplicada e ComputacionalComputational & Applied Mathematics v.28 n.3 20092009-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004en10.1590/S1807-03022009000300004 |
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Cai,Jing Chen,Guoliang An iterative method for solving a kind of constrained linear matrix equations system |
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Cai,Jing Chen,Guoliang |
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Cai,Jing |
title |
An iterative method for solving a kind of constrained linear matrix equations system |
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 |
iterative method for solving a kind of constrained linear matrix equations system |
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. |
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Sociedade Brasileira de Matemática Aplicada e Computacional |
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2009 |
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http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022009000300004 |
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