Modified Iteration Algorithm for Solving Absolute Value Equations

Abstract

A new iterative algorithm has been proposed in this study for the efficient solution of the absolute value equation (AVE). Through an equivalent transformation, the AVE has been restructured into a two-by-two block nonlinear equation, which led to the development of our new iteration method. The convergence characteristics and optimal parameters of this approach have been analyzed, and new convergence conditions, differing from previous findings, have been introduced. Numerical experiments have demonstrated that the proposed strategy is both feasible and effective.