A gradient-based iterative algorithm for generalized coupled Sylvester matrix equations over generalized centro-symmetric matrices

Abstract

An [Formula: see text] real matrix [Formula: see text] is said to be a symmetric orthogonal matrix if [Formula: see text]. An [Formula: see text] real matrix [Formula: see text] is called a generalized centro-symmetric matrix with respect to [Formula: see text], if [Formula: see text]. It is obvious that every [Formula: see text] matrix is also a generalized centro-symmetric matrix with respect to [Formula: see text] (identity matrix). In the present paper, we propose a gradient-based iterative algorithm to solve the generalized coupled Sylvester matrix equations [Formula: see text] over the generalized centro-symmetric matrix pair [Formula: see text]. It is proved that the iterative method is always convergent for any initial generalized centro-symmetric matrix pair [Formula: see text] Finally, a numerical example is discussed to illustrate the results.