A general fast shift-splitting iteration method for nonsymmetric saddle point problems

For nonsymmetric saddle point problems, the fast shift-splitting method and its generalized form are studied recently. In this paper, a general fast shift-splitting iteration method is proposed for solving nonsymmetric saddle point problems. The convergence and the semi-convergence of the proposed iteration method, respectively, for nonsingular and singular nonsymmetric saddle point problems are studied, respectively. Meanwhile, the spectral properties of the corresponding preconditioned matrix are analyzed in details. Numerical examples with experiments are given to show the robustness and the efficiency of the proposed method.