A generalization of the Newton-based matrix splitting iteration method for generalized absolute value equations

TL;DR

This paper introduces a generalized Newton-based matrix splitting iteration method for solving generalized absolute value equations, demonstrating convergence under mild conditions and improving upon existing methods with verified numerical effectiveness.

Contribution

The paper proposes a new GNMS method for GAVEs with weaker convergence conditions and confirms its efficiency through numerical experiments.

Findings

GNMS converges to the unique solution under mild conditions

Weaker convergence conditions are established for existing methods

Numerical results verify the effectiveness of the proposed method

Abstract

A generalization of the Newton-based matrix splitting iteration method (GNMS) for solving the generalized absolute value equations (GAVEs) is proposed. Under mild conditions, the GNMS method converges to the unique solution of the GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.