A modification of Newton method with third-order convergence

被引：102

作者：

Kou, Jisheng ^{[1
]}

Li, Yitian

Wang, Xiuhua

机构：

[1] Wuhan Univ, State Key Lab Water Resources & Hydropower Engn S, Wuhan 430072, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 181卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Newton method; third-order convergence; non-linear equations; root-finding; iterative method;

D O I：

10.1016/j.amc.2006.01.076

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself. Its practical utility is demonstrated by numerical examples. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1106 / 1111

页数：6

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