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.