An inexact Picard iteration method for absolute value equation

TL;DR

This paper introduces a new inexact Picard iteration method for solving absolute value equations, providing convergence conditions and demonstrating improved performance through numerical experiments.

Contribution

It proposes a novel inexact Picard iteration method with proven convergence conditions for absolute value equations, enhancing existing solution techniques.

Findings

The new method converges under specified conditions.

Numerical experiments show improved efficiency.

The approach outperforms previous methods.

Abstract

Recently, a class of inexact Picard iteration method for solving the absolute value equation: $Ax-|x~|=b$ have been proposed in [Optim Lett 8:2191-2202,2014]. To further improve the performance of Picard iteration method, a new inexact Picard iteration method is proposed to solve the absolute value equation. The sufficient conditions for the convergence of the proposed method for the absolute value equation is given. Some numerical experiments are given to demonstrate the effectiveness of the new method.