A NEW FAMILY OF MODIFIED NEWTON METHODS WITH CUBIC CONVERGENCE

被引：0

作者：

Lu, Yanjian ^{[1
]}

Xu, Xiubin ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

FIXED POINT THEORY | 2007年 / 8卷 / 01期

关键词：

Newton's method; order of convergence; iterative method; nonlinear equations; computational efficiency;

D O I：

暂无

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 family of modified Newton methods, which includes, as particular cases, some known results. It is proved that each method in the family is cubically convergent. A general error analysis is given, and the computational efficiency in term of function evaluations is provided. Numerical illustrations are given to compare the proposed methods with some other methods of the same kind.

引用

页码：47 / 57

页数：11

共 10 条

[1] Geometric constructions of iterative functions to solve nonlinear equations [J].

Amat, S ;

Busquier, S ;

Gutiérrez, JM .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 157 (01) :197-205

[2]

[Anonymous], 1984, RES NOTES MATH

[3] Modified Newton's method with third-order convergence and multiple roots [J].

Frontini, M ;

Sormani, E .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 156 (02) :345-354

[4] Some variant of Newton's method with third-order convergence [J].

Frontini, M ;

Sormani, E .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 140 (2-3) :419-426

[5]

Gautschi W., 1997, NUMERICAL ANAL INTRO

[6] On Newton-type methods with cubic convergence [J].

Homeier, HHH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 176 (02) :425-432

[7] A modified Newton method for rootfinding with cubic convergence [J].

Homeier, HHH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 157 (01) :227-230

[8]

KOU J, 2006, APPL MATH C IN PRESS

[9] Some new variants of Newton's method [J].

Özban, AY .

APPLIED MATHEMATICS LETTERS, 2004, 17 (06) :677-682

[10] 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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