On the convergence of inexact two-point Newton-like methods on Banach spaces

被引：5

作者：

Argyros, Ioannis Konstantinos ^{[1
]}

Alberto Magrenan, Angel ^{[2
]}

机构：

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

[2] Univ Int La Rioja, Escuela Ingn, Logrono 26002, La Rioja, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 265卷

关键词：

Inexact Newton-like methods; Banach space; Local convergence; Semilocal convergence; Divided difference of order one; Univariate unconstrained optimization; SEMILOCAL CONVERGENCE; 3RD-ORDER CONVERGENCE; RIEMANNIAN-MANIFOLDS; DYNAMICS; VARIANT; FAMILY;

D O I：

10.1016/j.amc.2015.05.127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a unified convergence analysis of Inexact Newton like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The convergence conditions are more general and the error analysis more precise than in earlier studies such as (Argyros, 2007: Catinas, 2005; Catinas, 1994; Chen and Yamamoto, 1989: Dennis, 1968: Hernandez and Romero, 2005; Potra and Ptak, 1984; Rheinboldt, 1977). Special cases of our results can be used to find zeros of derivatives. Numerical examples are also provided in this study. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：893 / 902

页数：10

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