Local convergence of Newton's method under majorant condition

2010/02/24 by O. P. Ferreira, Ferreira, O. P.
Mathematics · #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1002.4534

openalex publication_date 2010/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz condition on the operator under consideration, convergence, the biggest range for uniqueness of the solution, the optimal convergence radius and results on the convergence rate are established. Besides, two special cases of the general theory are presented as an application.

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