Matrix algorithms for solving the generalized coupled Sylvester and periodic coupled matrix equations

This paper is concerned with numerical solutions to the generalized coupled Sylvester matrix equations [Formula: see text] and the periodic coupled matrix equations [Formula: see text] which have many applications in several areas, such as control theory, stability theory, signal processing and perturbation analysis. By extending the bi-conjugate gradients (Bi-CG) and bi-conjugate residual (Bi-CR) methods, we obtain effective iterative algorithms for finding the solutions of the generalized coupled Sylvester and periodic coupled matrix equations. In order to compare these new algorithms with some existing methods, we present some numerical examples.