A generalization of the Gauss-Seidel iteration method for generalized absolute value equations

TL;DR

This paper introduces a parameter-free generalized Gauss-Seidel method for solving generalized absolute value equations, providing convergence analysis and numerical evidence of its effectiveness and efficiency.

Contribution

It develops a novel, parameter-free GGS method for generalized absolute value equations, extending recent related work and analyzing its convergence.

Findings

The GGS method converges under certain conditions.

Numerical results demonstrate the method's efficiency.

The method outperforms some existing approaches.

Abstract

A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the effectiveness and efficiency of the GGS method. Some results in the recent work of Edalatpour et al. \cite{edhs2017} are extended.