Parameterized generalized shift-splitting preconditioners for nonsymmetric saddle point problems

To solve nonsymmetric saddle point problems, the parameterized generalized shift-splitting (PGSS) preconditioner is presented and analyzed. The corresponding PGSS iteration method can be applied not only to the nonsingular saddle point problems but also to the singular ones. The convergence and semi-convergence of the PGSS iteration method are discussed carefully. Meanwhile, the spectral properties of the preconditioned matrix and the strategy of the choices of the parameters are given. Numerical experiments further demonstrate that the PGSS iteration method and the PGSS preconditioner are efficient and have better performance than some existing iteration methods and newly proposed preconditioners, respectively, for solving both the nonsingular and singular nonsymmetric saddle point problems.