An Improved Error Analysis for the Secant Method Under the Gamma Condition

被引：0

作者：

Argyros, Ioannis K. ^{[1
]}

机构：

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

来源：

PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS | 2007年 / 39卷

关键词：

Banach space; Secant method; Newton's method; Gamma condition; majorizing sequence; semilocal convergence; radius of convergence; Newton-Kantorovich theorem;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide sufficient convergence conditions for the Secant method for approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is a type of gamma condition first introduced in [9] for the study of Newton's method. Our sufficient convergence condition reduces to the one obtained in [12] for Newton's method although in general it can be weaker. A numerical example is also provided.

引用

页码：1 / 11

页数：11

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