Two conditions concerning Newton's method

被引：2

作者：

Wu, Min ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 194卷 / 01期

关键词：

Newton's method; majorizing function; center Lipschitz condition;

D O I：

10.1016/j.amc.2007.04.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we compare two conditions concerning Newton's method, and find out that even under some weaker condition one has the convergence of the Newton's method and a better error bound than the relative strong condition. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：102 / 107

页数：6

共 50 条

[41] On Newton's method of approximation
Fine, HB
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1916, 2 : 546 - 552
[42] On the extended Newton's method
Berinde, V
ADVANCES IN DIFFERENCE EQUATIONS-BOOK, 1997, : 81 - 88
[43] IMPLEMENTING NEWTON'S METHOD
Neuerburg, Kent M.
MISSOURI JOURNAL OF MATHEMATICAL SCIENCES, 2007, 19 (02) : 131 - 140
[44] Generalizations of Newton's method
Gilbert, WJ
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2001, 9 (03) : 251 - 262
[45] Continuous Newton's Method
Neuberger, J. W.
SOBOLEV GRADIENTS AND DIFFERENTIAL EQUATIONS, SECOND EDITION, 2010, 1670 : 79 - 83
[46] ON NEWTON METHOD UNDER MILD DIFFERENTIABILITY CONDITIONS
ARGYROS, IK
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 1990, 15 (2A): : 233 - 239
[47] Modified Newton's method and dual method through rational approximation at two expanded points
Sui, Yunkang
Yang, Zhiguang
Dalian Ligong Daxue Xuebao/Journal of Dalian University of Technology, 1994, 34 (01):
[48] LOCAL CONVERGENCE OF THE NEWTON'S METHOD IN TWO STEP NILPOTENT LIE GROUPS
Dali, Bechir
Guediri, Mohammed
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2022, 6 (03): : 199 - 212
[49] Concerning the "terra incognita" between convergence regions of two Newton methods
Argyros, IK
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (01) : 179 - 194
[50] On the R-order of convergence of Newton's method under mild differentiability conditions
Ezquerro, J. A.
Hernandez, M. A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 197 (01) : 53 - 61

← 1 2 3 4 5 →