The modified shift-splitting preconditioners for nonsymmetric saddle-point problems

For a nonsymmetric saddle-point problem, a modified shift-splitting (MSS) preconditioner is proposed based on a splitting of the nonsymmetric saddle-point matrix. By removing the shift term of the (1,1)(1,1)-block of the MSS preconditioner, a local MSS (LMSS) preconditioner is also presented. Both of the two preconditioners are easy to be implemented since they have simple block structures. The convergence properties of the two iteration methods induced respectively by the MSS and the LMSS preconditioners are carefully analyzed. Numerical experiments are illustrated to show the robustness and efficiency of the MSS and the LMSS preconditioners used for accelerating the convergence of the generalized minimum residual method.