New variants of Jarratt's method with sixth-order convergence
type: Item
instance of: scholarly article
title: New variants of Jarratt's method with sixth-order convergence
zbMATH Open document ID: 1187.65052
author: Hongmin Ren
author: Weihong Bi
author: Qingbiao Wu
published in: Numerical Algorithms
publication date: 2010-01-04T00:00:00Z
review text: The authors propose some new variants of the Jarratt method with sixth-order convergence for solving univariate nonlinear equations. \textit{P. Jarratt} modified the Newton method and proposed a fourth order multipoint iterative scheme for solving equations. Math. Comput. 20, 434--437 (1966; Zbl 0229.65049)]. Since then the Newton-Jarratt method has been widely studied for nonlinear equations, see \textit{J. Argyros} [J. Appl. Math. Comput. 28, No.~1--2, 15--28 (2008; Zbl 1159.65055)]. Further, \textit{J. Kou} and \textit{Y. Li} [Appl. Math. Comput. 189, No.~2, 1816--1821 (2007; Zbl 1122.65338)] have also proposed an improvement of the Jarratt method wherein the local order of convergence is improved from four for Jarratt method to six for the new method. The authors have not established a better accuracy in the present paper as compared to that of Kou and Li [loc. cit.].
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 5652344
zbMATH Keywords: nonlinear equations
zbMATH Keywords: iterative methods
zbMATH Keywords: order of convergence
zbMATH Keywords: two variable Taylor expansion
zbMATH Keywords: Jarratt method
MaRDI profile type: Publication
full work available at URL: s11075-009-9302-3
OpenAlex ID: W1985698733
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DOI: 10.1007/S11075-009-9302-3
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description: scientific article; zbMATH DE number 5652344