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

Authors:
Mehdi Dehghan;Masoud Hajarian
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran 15914, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran 15914, Iran
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

A matrix P@?R^n^x^n is said to be a symmetric orthogonal matrix if P=P^T=P^-^1. A matrix A@?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.