A family of modified super-Halley methods with fourth-order convergence

被引：14

作者：

Kou, Jisheng ^{[1
]}

Li, Yitian

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

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

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 189卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Super-Halley method; Nwton's method; non-linear equations; iterative method;

D O I：

10.1016/j.amc.2006.11.092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a family of modified super-Halley methods for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. The superiority of the new methods is that they require no additional evaluations of the function, the first derivative or second derivative as compared with the classical third-order methods although their order is improved. Numerical results show that the new methods can be efficient. (c) 2006 Published by Elsevier Inc.

引用

页码：366 / 370

页数：5

共 8 条

[1]

CHEN D, 1994, APPL MATH LETT, V7

[2] Solving nonlinear integral equations arising in radiative transfer [J].

Ezquerro, JA ;

Gutiérrez, JM ;

Hernández, MA ;

Salanova, MA .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1999, 20 (7-8) :661-673

[3]

Gautschi W., 1997, NUMERICAL ANAL INTRO

[4] An improvement to Ostrowski root-finding method [J].

Grau, M ;

Díaz-Barrero, JL .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) :450-456

[5] An acceleration of Newton's method:: Super-Halley method [J].

Gutiérrez, JM ;

Hernández, MA .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 117 (2-3) :223-239

[6]

KOU JS, 2006, APPL MATH COMPUT

[7]

Ostrowski A., 1973, Solution of Equations in Euclidean and Banach Spaces

[8] A variant of Newton's method with accelerated third-order convergence [J].

Weerakoon, S ;

Fernando, TGI .

APPLIED MATHEMATICS LETTERS, 2000, 13 (08) :87-93

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