A generalization of the local Hermitian and skew-Hermitian splitting iteration methods for the non-Hermitian saddle point problems

For large sparse saddle point problems, Jiang and Cao studied a class of local Hermitian and skew-Hermitian splitting (LHSS) iteration methods (see M.-Q. Jiang, Y. Cao, On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math. 231 (2009) 973–982). In this paper, we generalized these methods and propose a class of generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration schemes for solving the non-Hermitian saddle point problems. We derive conditions for guaranteeing the convergence of these iterative methods. With different choices of the parameter matrices, the generalized iterative methods lead to a series of existing and new iterative methods. Numerical experiments for a model Stokes problem are provided, further show that the new iteration methods are feasible and effective.