On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation AXB=CAXB=C

In this paper, a Hermitian and skew-Hermitian splitting (HSS) iteration method for solving the linear matrix equation AXB=CAXB=C is proposed. This method is formed by extending the corresponding HSS iteration method for solving Ax=bAx=b. The analysis shows that the HSS iteration method will converge under certain assumptions. Moreover, the optimal parameter of this iteration method is presented. Numerical results show that this new method is more efficient and robust than existing methods.