A new SOR-Like method for the saddle point problems

In previous years, Golub, Wu and Yuan presented a generalized successive over-relaxation (SOR-Like) method for solving the saddle point problems. In this paper, we present a new SOR-Like (NSOR-Like) method which has three parameters. Our new method can be applied to the nonsingular saddle point problems as well as the singular cases. The characteristic of eigenvalues of the iteration matrix of this NSOR-Like method is analyzed. Then we give the convergence (semi-convergence) theorem of the new iterative method by giving the restrictions imposed on the parameter. Moreover, that convergence (semi-convergence) theorem is applied to some special cases to give the convergence region for the parameters. We can see that NSOR-Like method has a wider convergence (semi-convergence) region for ωω and ττ than the Parameterized Uzawa method which covers Preconditioned Uzawa method and Uzawa method. In addition, the optimal iteration parameters and the corresponding convergence (semi-convergence) factor for the Uzawa method are presented.