Ball convergence for Steffensen-type fourth-order methods

被引：13
|
作者：
Argyros, Ioannis K. [1 ]
George, Santhosh
机构：
[1] Cameron Univ, Math, Lawton, OK 73505 USA
来源：
INTERNATIONAL JOURNAL OF INTERACTIVE MULTIMEDIA AND ARTIFICIAL INTELLIGENCE | 2015年 / 3卷 / 04期
关键词：
Newton method; Steffensen-type methods; order of convergence; local convergence;
D O I：
10.9781/ijimai.2015.347
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.
引用
收藏
页码：37 / 42
页数：6
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