Local convergence analysis of inexact Newton-like methods under majorant condition

TL;DR

This paper analyzes the local convergence of inexact Newton-like methods for solving nonlinear equations, establishing convergence conditions under a majorant function that relaxes traditional Lipschitz assumptions.

Contribution

It introduces a convergence analysis framework based on majorant conditions, extending the understanding of inexact Newton-like methods beyond Lipschitz continuity.

Findings

Provides an estimate of the convergence radius.

Establishes a relationship between the majorant function and the nonlinear operator.

Includes special cases of the convergence analysis.

Abstract

We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases