Finite iterative algorithm for solving the generalized coupled Sylvester – conjugate matrix equations

Abstract

In this paper, we consider an iterative algorithm for solving a generalized coupled Sylvester– conjugate matrix equation. With the iterative algorithm, the existence of a comman solution of these two matrix equation can be determined automatically. When these two matrix equations are consistent, for any initial matrices  the solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round off errors.  Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to illustrate the effectiveness of the proposed method and to support the theoretical results of this paper.