SSOR-like methods for saddle point problems

Abstract

Saddle point problems arise in a wide variety of applications in computational and engineering. The aim of this paper is to present a SSOR-like iterative method for solving the saddle point problems. Here the convergence of this method is studied and specifically, the spectral radius and the optimal relaxation parameter of the iteration matrix are also investigated. Numerical experiments show that the SSOR-like method with a proper preconditioning matrix is better than SOR-like method presented by Golub et al. [G.H. Golub, X. Wu, and J.-Y. Yuan, SOR-like methods for augmented systems, BIT 41 (2001), pp. 71–85].

Keywords:

• SSOR-like method
• augmented system
• saddle point problem
• Stokes equations
• convergence

2000 AMS Subject Classification :

• 65F10

Acknowledgements

Bing Zheng was supported by the start-up fund of Lanzhou University and the Natural Science Foundation of Gansu Province (3ZS051-A25-020), People's Republic of China. Ke Wang was supported by the China Postdoctoral Science Foundation (No. 20060400634). The authors are very grateful to the referees for their valuable suggestions that help to improve the quality of the paper.