On the Alternative SOR-like Iteration Method for Solving Absolute Value Equations

Abstract

In this paper, by equivalently reformulating the absolute value equation (AVE) into an alternative two-by-two block nonlinear equation, we put forward an alternative SOR-like (ASOR-like) iteration method to solve the AVE. The convergence of the ASOR-like iteration method is established, subjecting to specific restrictions placed on the associated parameter. The selection of the optimal iteration parameter is investigated theoretically. Numerical experiments are given to validate the feasibility and effectiveness of the ASOR-like iteration method.