On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses

被引：5

作者：

Argyros, Ioannis K. ^{[1
]}

Hilout, Said ^{[2
]}

机构：

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

[2] Univ Poitiers, Lab Math & Applicat, F-86962 Futuroscope, France

来源：

MATHEMATICA SLOVACA | 2013年 / 63卷 / 03期

关键词：

Newton's method; Banach space; majorizing sequences; Lipschitz/center-Lipschitz condition; local/semilocal convergence; radius of convergence; Kantorovich hypothesis; SEMILOCAL CONVERGENCE;

D O I：

10.2478/s12175-013-0123-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide new local and semilocal convergence results for Newton's method in a Banach space. The sufficient convergence conditions do not include the Lipschitz constant usually associated with Newton's method. Numerical examples demonstrating the expansion of Newton's method are also provided in this study.

引用

页码：621 / 638

页数：18

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