An improvement of Chebyshev-Halley methods free from second derivative

被引：30

作者：

Li, Dingfang ^{[1
]}

Liu, Ping ^{[1
]}

Kou, Jisheng ^{[2
]}

机构：

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

[2] Hubei Engn Univ, Sch Math & Stat, Xiaogan 432000, Hubei, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 235卷

基金：

美国国家科学基金会;

关键词：

Chebyshev-Halley method; Newton method; Non-linear equations; Iterative method; Root-finding; NONLINEAR EQUATIONS; BANACH-SPACES; CONVERGENCE; FAMILY;

D O I：

10.1016/j.amc.2014.02.083

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a family of modified Chebyshev-Halley's methods free from second derivative is presented. Per iteration the new methods require three evaluations of the function and one of its first derivatives. A detailed convergence analysis of the new methods shows that the new methods are at least fifth-order convergent and especially, the modified super-Halley's method is sixth-order convergent. Numerical examples are given to illustrate the efficiency and performance of the new methods. (C) 2014 Published by Elsevier Inc.

引用

页码：221 / 225

页数：5

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