An inexact framework of the Newton-based matrix splitting iterative method for the generalized absolute value equation

TL;DR

This paper introduces an inexact Newton-based matrix splitting iterative method for solving generalized absolute value equations, demonstrating its global linear convergence and superior performance through numerical experiments.

Contribution

It develops an inexact framework for the Newton-based matrix splitting method, extending previous exact methods and providing convergence analysis and numerical validation.

Findings

The INMS method converges globally linearly.

Numerical results show INMS outperforms existing methods.

The framework broadens the applicability of Newton-based splitting techniques.

Abstract

An inexact framework of the Newton-based matrix splitting (INMS) iterative method is developed to solve the generalized absolute value equation, whose exact version was proposed by Zhou, Wu and Li [H.-Y. Zhou, S.-L. Wu and C.-X. Li, \textit{J. Comput. Appl. Math.}, 394 (2021), 113578]. Global linear convergence of the INMS iterative method is investigated in detail. Some numerical results are given to show the superiority of the INMS iterative method.