Three new optimal fourth-order iterative methods to solve nonlinear equations
type: Item
instance of: scholarly article
title: Three new optimal fourth-order iterative methods to solve nonlinear equations
zbMATH Open document ID: 1268.65065
DOI: 10.1155/2013/957496
author: Gustavo Fernández-Torres
author: Juan Vásquez-Aquino
published in: Advances in Numerical Analysis
publication date: 2013-06-07T00:00:00Z
review text: Summary: We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture (cf. [\textit{H. T. Kung} and \textit{J. F. Traub}, J. Assoc. Comput. Mach. 21, 643--651 (1974; Zbl 0289.65023)]), these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6171670
zbMATH Keywords: Newton's method
zbMATH Keywords: nonlinear equations
zbMATH Keywords: Kung-Traub conjecture
zbMATH Keywords: multiple roots
zbMATH Keywords: numerical examples
zbMATH Keywords: fourth-order convergence
Wikidata QID: Q58919041
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/957496
OpenAlex ID: W2073862053
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DBLP publication ID: journals/ana/TorresV13
description: scientific article; zbMATH DE number 6171670