Generalized SOR-like iteration method for solving weakly nonlinear systems

Abstract

The generalized successive overrelaxation method is an efficient tool for solving a class of two-by-two augmented systems. In this paper, we transform the weakly nonlinear equations into the form of such two-by-two augmented systems. By applying the generalized successive overrelaxation method to this augmented system, we develop a class of generalized successive overrelaxation like iteration methods for solving the weakly nonlinear equations. Under some reasonable assumptions on the matrix splitting and two relaxation parameters, we are able to establish the global convergence results of the proposed methods. As a by-product, we improve the existing convergence results of the successive overrelaxation like iteration methods in terms of giving a weaker convergence condition. Finally, we present numerical results to demonstrate the usefulness and efficiency of the proposed methods.

Keywords:

• Weakly nonlinear equations
• linear complementarity problem
• matrix splitting
• SOR
• relaxation parameter

2020 AMS Subject Classifications:

• 65H10
• 65F10

Acknowledgments

We would also like to thank the referees for a number of very helpful and insightful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 12001531] and the undergraduate innovation and entrepreneurship training programs of Beijing [grant number S202110019192].