Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space

被引：38

作者：

Wu, Qingbiao ^{[1
]}

Zhao, Yueqing

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310028, Zhejiang, Peoples R China

[2] Taizhou Univ, Dept Math, Linhai 317000, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 175卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Newton-Kantorovich theorem; Banach space; nonlinear operator equation; modified Newton method; majorizing function;

D O I：

10.1016/j.amc.2005.08.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following the ideas of Frontini and Sormani, we present a modified Newton method in Banach space which is used to solve the nonlinear operator equation. We establish the Newton-Kantorovich convergence theorem for the modified Newton method with third-order convergence in Banach space by using majorizing function. We also get the error estimate. Finally, two examples are provided to show the application of our theorem. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：1515 / 1524

页数：10

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