Finite iterative Hermitian R-conjugate solutions of the generalized coupled Sylvester-conjugate matrix equations

In this paper, an iterative algorithm for solving a generalized coupled Sylvester-conjugate matrix equations over Hermitian R-conjugate matrices given by A(1)VB(1)+C1WD1 = E-1(V) over barF(1) + G(1) and A(2)VB(2) + C2WD2 = E-2(V) over barF(2) + G(2) is presented. When these two matrix equations are consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial arbitrary Hermitian R-conjugate solution matrices V-1, W-1. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to demonstrate the behavior of the proposed method and to support the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.