The improvements of modified Newton's method

被引：43

作者：

Kou, Jisheng ^{[1
]}

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：

Newton's method; non-linear equations; root-finding; iterative method;

D O I：

10.1016/j.amc.2006.11.115

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we improve some third-order modifications of Newton's method and obtain many new methods for solving non-linear equations. The new methods have the order of convergence five or six. Per iteration these methods require two evaluations of the function and two evaluations of its first derivative and therefore the efficiency of the new methods may also be improved. These methods can compete with Newton's method, as we show in some examples. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：602 / 609

页数：8

共 12 条

[1] Third-order methods from quadrature formulae for solving systems of nonlinear equations [J].

Frontini, A ;

Sormani, E .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 149 (03) :771-782

[2] 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

[3] 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

[4]

Gautschi W., 1997, NUMERICAL ANAL INTRO

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

Homeier, HHH .

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

[6] A modified Newton method with cubic convergence: the multivariate case [J].

Homeier, HHH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 169 (01) :161-169

[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 JS, 2006, J COMPUT APPL MATH

[9]

KOU JS, IN PRESS J COMPUT AP

[10]

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

← 1 2 →