Generalized fast shift-splitting preconditioner for nonsymmetric saddle-point problems

For nonsingular and singular nonsymmetric saddle-point problems, Dou, Yin, and Liao proposed a fast shift-splitting preconditioner by combining shift-splitting technique and Hermitian and skew-Hermitian (HSS) splitting technique. In this paper, a generalized fast shift-splitting (GFSS) preconditioner is derived. The convergence and semi-convergence properties of the new shift-splitting iteration method are analyzed for solving the nonsingular and singular nonsymmetric saddle-point problems, respectively. Furthermore, the spectral properties of the GFSS preconditioned matrix are given. Finally, some numerical examples are carried out to demonstrate the robustness and effectiveness of our new preconditioner on nonsingular and singular nonsymmetric saddle-point problems.