The (R, S)-symmetric least squares solutions of the general coupled matrix equations

Abstract

Let and be two real symmetric orthogonal matrices. An real matrix is said to be an -symmetric matrix if . The -symmetric matrices have been widely used in engineering and scientific computing. In this paper, we construct an algorithm to solve the general coupled matrix equations , where is a -symmetric matrix. The algorithm produces suitable such that is minimized within a finite number of iteration steps in the absence of round-off errors. We show that the algorithm is stable any case. The algorithm requires little storage capacity. Numerical examples are given to show that the algorithm is efficient.