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

页码：583 / 589

页数：7

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