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.
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页码：821 / 828
页数：8
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