Two-parameter GSOR method for the augmented system

Abstract

A new iterative method is given for the augmented system of equations. Similarly to the GSOR and SOR-like methods, the new method involves two iteration parameters and one preconditioning matrix. The convergence analysis and the determination of the optimum parameters are studied first. Then the explicit formulae for the optimum parameters and the associated spectral radius are derived. Finally, numerical computations are presented which show clearly that the new method has a very good numerical performance and is much faster than the SOR-like method.

Keywords:

• GSOR method
• SOR-like method
• Augmented system
• Saddle-point problem
• Stokes equation

Acknowledgements

This work was supported by the National Nature Science Foundation of China (10471019).