Parameterized preconditioned Hermitian and skew-Hermitian splitting iteration method for a class of linear matrix equations

Recently, Wang et al. (2013) proposed an efficient Hermitian and skew-Hermitian splitting   (HSS) iteration method to approximate the solution of linear matrix equation. To further improve the efficiency of the HSS method, we in this paper establish a parameterized preconditioned HSS (PPHSS) iteration method by introducing two Hermitian positive definite preconditioners and two more different iteration parameters for the HSS method. The convergence properties of the PPHSS method used for solving linear matrix equation AXB=CAXB=C are strictly analyzed and the quasi-optimal values of the iteration parameters for the PPHSS method are also derived. Numerical results demonstrate the feasibility and the efficiency of the PPHSS iteration method.