科研之友
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摘要
An efficient iterative algorithm is presented to solve a system of linear matrix equations A(1)X(1)B(1) + A(2)X(2)B(2) = E, C1X1D1 + C2X2D2 = F When the system is consistent, for any initial matrices X-1(0) and X-2(0), a solution can be obtained in the absence of roundoff errors, and the least norm solution can be obtained by choosing a special kind of initial matrix. In addition, the unique optimal approximation solutions (X) over cap (1) and (X) over cap (2) to the given matrices (X) over tilde (1) and (X) over tilde (2) in Frobenius norm can be obtained by finding the least norm solution of a new pair of matrix equations A(1)(X) over bar B-1(1) + A(2)(X) over bar B-2(2) = (E) over bar, C-1(X) over bar D-1(1) + C-2(X) over bar D-2(2) = (F) over bar, where (E) over bar - A(1)(X) over tilde B-1(1) - A(2)(X) over tilde B-2(2), (F) over bar = F - C-1(X) over tilde D-1(1) - C-2(X) over tilde D-2(2) The given numerical example demonstrates that the iterative algorithm is efficient. Especially, when the numbers of the parameter matrices A(1),A(2),B-1,B-2,C-1,C-2,D-1,D-2, are large, our algorithm is efficient as well.
