A Technique to Composite a Modified Newton's Method for Solving Nonlinear Equations

2011/06/06 by Miquel Grau-Sánchez, Grau-Sánchez, Miquel, José Luis Díaz‐Barrero +1
Computer Science · Mathematics · #41A25 #65H05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1106.0996

openalex publication_date 2011/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index.

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