Modified SOR-like method for the augmented system

Abstract

The SOR-like method with two real parameters ω and α is considered for solving the augmented system. The new method is called the modified SOR-like method (MSOR-like method). The MSOR-like method becomes the SOR-like method when α = 0. The functional equation relating the parameters and eigenvalues of the iteration matrix of the MSOR-like method is obtained. Hence the necessary and sufficient condition for the convergence of the GSOR-like method is derived. It is shown that when α is negative, the convergence domain for the parameter ω for the MSOR-like method is larger than that for the SOR-like method. Finally, a numerical computation based on a particular linear system is given which clearly shows that the MSOR-like method outperforms the SOR-like method.

^†In memory of Professor D.J. Evans.

Keywords:

• SOR-like method
• MSOR-like method
• Saddle-point problem
• Augmented system
• Iterative method

Acknowledgements

The authors are indebted to the referees for their valuable suggestions, which improved the quality of the paper.

Notes

^†In memory of Professor D.J. Evans.