An iterative algorithm for solving a pair of matrix equations AYB=E,CYD=F over generalized centro-symmetric matrices

AbstractA matrix P∈Rn×n is said to be a symmetric orthogonal matrix if P=PT=P−1. A matrix A∈Rn×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 Y1, the sequence {Yk} 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