An iterative method for the bisymmetric solutions of the consistent matrix equations A 1 XB 1=C 1, A 2 XB 2=C 2

Abstract

In this paper, an iterative method is presented for finding the bisymmetric solutions of a pair of consistent matrix equations A 1 XB 1=C 1, A 2 XB 2=C 2, by which a bisymmetric solution can be obtained in finite iteration steps in the absence of round-off errors. Moreover, the solution with least Frobenius norm can be obtained by choosing a special kind of initial matrix. In the solution set of the matrix equations, the optimal approximation bisymmetric solution to a given matrix can also be derived by this iterative method. The efficiency of the proposed algorithm is shown by some numerical examples.