An iterative algorithm for solving a pair of matrix equations AYB = E, CYD = F over generalized centro-symmetric matrices
A matrix P is an element of R(n) (x) (n) is said to be a symmetric orthogonal matrix if P = p(T) = P(-1). A matrix A is an element of R(n x n) is said to be generalized centro-symmetric (generalized central anti-symmetric) with respect to P, if A = PAP (A = -PAP). The generalized centro-symmetric matrices have wide applications in information theory, linear estimate theory and numerical analysis. In this paper, we propose a new iterative algorithm to compute a generalized centro-symmetric solution of the linear matrix equations AYB = E, CYD = F. We show, when the matrix equations are consistent over generalized centro-symmetric matrix Y, for any initial generalized centro-symmetric matrix Y(1), the sequence [Y(k)] generated by the introduced algorithm converges to a generalized centro-symmetric solution of matrix equations AYB = E. CYD = F. The least Frobenius norm generalized centro-symmetric solution can be derived when a special initial generalized centro-symmetric matrix is chosen. Furthermore, the optimal approximation generalized centro-symmetric solution to a given generalized centro-symmetric matrix can be derived. Several numerical examples are given to show the efficiency of the presented method. (C) 2008 Elsevier Ltd. All rights reserved.
matrix equations symmetric orthogonal matrix generalized centro-symmetric matrix least frobenius norm generalized centro-symmetric solution iterative method