An iterative method for solving a kind of constrained linear matrix equations system
نویسندگان
چکیده
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 ∈ S = {X |X = U (X)}, where Ai is a linear operator from Cm×n onto C pi ×qi , Ei ∈ C pi ×qi , 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 ∈ S , 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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