On The Iterative Algorithms For Large Sparse Saddle Point Problems

In this paper, we mainly study the iterative algorithms for large sparse saddle point problems(SPP). This kind of problems arise from many areas of scientific research and engineering computations, such as computational fluid dynamics, constrained optimization and constrained and weighted least square problems. Therefore, it is of great interest to develop fast and efficient iterative methods for such kind of problems. In this paper, we first introduce the SOR-like iterative scheme. Then, based on the SSOR splitting, we present the SSOR-like iterative scheme. The convergence results are also given. The numerical results show that our new method is more efficient than SOR-like method.By introducing some new parameters, we can further accelerate the convergence speed of the iterative algorithms. In this paper we give a kind of generalized SOR(GSOR) method and generalized AOR(GAOR) method. Under some suitable conditions, we give the convergence results. Numerical results show that the new methods are very effective.