A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems

In this paper, we propose a new preconditioned generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration method for solving the non-Hermitian saddle point problems. The semi-convergence of this method is discussed. Theoretical analysis shows that the semi-convergence of this new method can be guaranteed by suitable choices of the parameters and parameter matrices. Numerical examples are used to illustrate the theoretical results and examine the numerical effectiveness of the GLHSS iteration method served either as a preconditioner for GMRES or as a solver.