An optimal Steffensen-type family for solving nonlinear equations

被引：72
|
作者：
Zheng, Quan [1 ]
Li, Jingya [1 ]
Huang, Fengxi [1 ]
机构：
[1] N China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 23期
关键词：
Nonlinear equation; Newton's method; Steffensen's method; Derivative free; Optimal convergence;
D O I：
10.1016/j.amc.2011.04.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a general family of Steffensen-type methods with optimal order of convergence for solving nonlinear equations is constructed by using Newton's iteration for the direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub [H. T. Kung, J.F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Math. 21 (1974) 634-651] that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2(m-1). Its error equations and asymptotic convergence constants are obtained. Finally, it is compared with the related methods for solving nonlinear equations in the numerical examples. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：9592 / 9597
页数：6
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