The Newton method for operators with Holder continuous first derivative

被引：40

作者：

Hernández, MA ^{[1
]}

机构：

[1] Univ La Rioja, Dept Math & Computat, Logrono, Spain

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2001年 / 109卷 / 03期

关键词：

nonlinear equations in Banach spaces; Newton method; semilocal convergence theorem; recurrence relations; a priori error bounds; Hammerstein integral equation;

D O I：

10.1023/A:1017571906739

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We analyze the convergence of the Newton method when the first Frechet derivative of the operator involved is Holder continuous. We calculate also the R-order of convergence and provide some a priori error bounds. Based on this study, we give some results on the existence and uniqueness of the solution for a nonlinear Hammerstein integral equation of the second kind.

引用

页码：631 / 648

页数：18

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