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 A1VB1+C1WD1=E1V¯F1+G1 and A2VB2+C2WD2=E2V¯F2+G2 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 V1, W1. 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.