On convergence of a new secant-like method for solving nonlinear equations

被引：8
|
作者：
Ren, Hongmin [1 ]
Wu, Qingbiao [2 ]
Bi, Weihong [2 ]
机构：
[1] Hangzhou Radio & TV Univ, Dept Elect & Informat, Hangzhou 310012, Zhejiang, Peoples R China
[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Iterative method; Secant-like method; Convergence order; Error estimate; Generalized Fibonacci sequence; NEWTONS METHOD; BALL;
D O I：
10.1016/j.amc.2010.05.092
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：583 / 589
页数：7
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