Certain improvements of Newton's method with fourth-order convergence

被引：15

作者：

Chun, Changbum ^{[1
]}

Neta, Beny ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[2] USN, Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 02期

关键词：

Newton's method; Iterative methods; Nonlinear equations; Order of convergence; Method of undetermined coefficients; Root-finding methods; ITERATIVE METHOD; CONSTRUCTION; VARIANTS; FAMILY;

D O I：

10.1016/j.amc.2009.06.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present two new schemes, one is third-order and the other is fourth-order. These are improvements of second-order methods for solving nonlinear equations and are based on the method of undetermined coefficients. We show that the fourth-order method is more efficient than the fifth-order method due to Kou et al. [J. Kou, Y. Li, X. Wang, Some modi. cations of Newton's method with fifth-order covergence, J. Comput. Appl. Math., 209 (2007) 146-152]. Numerical examples are given to support that the methods thus obtained can compete with other iterative methods. Published by Elsevier Inc.

引用

页码：821 / 828

页数：8

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