Iterative solutions to matrix equations of the form AiXBi=FiAiXBi=Fi

This paper is concerned with the numerical solutions to the linear matrix equations A1XB1=F1A1XB1=F1 and A2XB2=F2A2XB2=F2; two iterative algorithms are presented to obtain the solutions. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. Finally, simulation examples are given to verify the proposed convergence theorems.