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

作者：Dehghan Mehdi^*; Hajarian Masoud

来源：Computers & Mathematics with Applications, 2008, 56(12): 3246-3260.

DOI：10.1016/j.camwa.2008.07.031

• Matrix equations
• Iterative method
• Generalized centro-symmetric matrix
• Least Frobenius norm generalized centro-symmetric solution
• Symmetric orthogonal matrix

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.

• 出版日期2008-12