A finite iterative algorithm for the solution of Sylvester-conjugate matrix equations AV+BW=EV¯F+C and AV+BW¯=EV¯F+C

Abstract

In this paper, we consider two iterative algorithms for the Sylvester-conjugate matrix equation $AV+BW=E\overline{V}F+C$ and $AV+B\overline{W}=E\overline{V}F+C$. When these two matrix equations are consistent, for any initial matrices the solutions can be obtained 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. Two numerical examples are given to illustrate the effectiveness of the proposed method.