A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Frechet-derivative

被引：7

作者：

Argyros, IK ^{[1
]}

机构：

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 130卷 / 1-2期

关键词：

Newton's method; Banach space; global convergence; Frechet-derivative; Kantorovich hypothesis;

D O I：

10.1016/S0377-0427(00)00330-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new global Kantorovich-type convergence theorem for Newton's method in Banach space is provided for approximating a solution of a nonlinear equation. It is assumed that a solution exists and the second Frechet-derivative of the operator involved satisfies a Lipschitz condition. Our convergence condition differs from earlier ones, and therefore it has theoretical and practical value. Finally, a simple numerical example is provided to show that our results apply, where earlier ones fail. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：369 / 373

页数：5