A cubic-order variant of Newton's method for finding multiple roots of nonlinear equations

被引：9

作者：

Kim, Young Ik ^{[1
]}

Geum, Young Hee ^{[1
]}

机构：

[1] Dankook Univ, Dept Appl Math, Cheonan 330714, South Korea

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 04期

关键词：

Multiple root; Order of convergence; Newton's method; Nonlinear equation; Root finding; FAMILY;

D O I：

10.1016/j.camwa.2011.04.069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A second-derivative-free iteration method is proposed below for finding a root of a nonlinear equation f (x) = 0 with integer multiplicity m >= 1: x(n+1) = x(n) - f(x(n) - mu f(x(n))/f'(x(n))) + gamma f(x(n))/f'(x(n)), n = 0, 1, 2, .... We obtain the cubic order of convergence and the corresponding asymptotic error constant in terms of multiplicity m, and parameters mu and gamma. Various numerical examples are presented to confirm the validity of the proposed scheme. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1634 / 1640

页数：7

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