The generalized HSS method for solving singular linear systems

For the singular, non-Hermitian, and positive semidefinite linear systems, we propose an alternating-direction iterative method with two parameters based on the Hermitian and skew-Hermitian splitting. The semi-convergence analysis and the quasi-optimal parameters of the proposed method are discussed. Moreover, the corresponding preconditioner based on the splitting is given to improve the semi-convergence rate of the GMRES method. Numerical examples are given to illustrate the theoretical results and the efficiency of the generalized HSS method either as a solver or a preconditioner for GMRES.