Numerical Method For Solving Large Sparse Singular Saddle Point Problems

Saddle point problems are widely involved in many areas of scientific research and engineering computations, such as computational fluid dynamics, mixed finite element approximation of elliptic partial differential equations, optimal control, weighted least-squares problems, electro magnetics and so on. Because these problems have such a wide application source and value, it is of great interest to develop fast and efficient methods.In this paper, for solving the singular saddle point problem, a new preconditioned ac-celerated Hermitian and skew-Hermitian (PAHSS) splitting iteration method is presented. A sufficient condition for guaranteeing the semi-convergence of this iteration method are given. In addition, if the iteration parameters a and β approximate to∞, all eigenval-ues approach1. Finally, we propose two numerical examples, one is a particular linear system, the other is a linear algebra system based on the Stokes equation. The numerical results show that this new method is feasible and effective.