Three-step iterative methods with optimal eighth-order convergence

被引：57

作者：

Cordero, Alicia ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

Vassileva, Maria P. ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain

[2] Inst Tecnol Santo Domingo INTEC, Santo Domingo, Dominican Rep

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 10期

关键词：

Nonlinear equations; Iterative methods; Convergence order; Efficiency index; Ostrowski's method; Optimal order; FAMILY;

D O I：

10.1016/j.cam.2011.01.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub's conjecture. Numerical comparisons are made to show the performance of the new family. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：3189 / 3194

页数：6

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