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

共 13 条

[1] Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Bi, Weihong
Ren, Hongmin
Wu, Qingbiao
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) : 105 - 112
[2] Some sixth-order variants of Ostrowski root-finding methods
Chun, Changbum
Ham, YoonMee
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (02) : 389 - 394
[3] New modifications of Potra-Ptaks method with optimal fourth and eighth orders of convergence
Cordero, Alicia
Hueso, Jose L.
Martinez, Eulalia
Torregrosa, Juan R.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (10) : 2969 - 2976
[4] An improvement to Ostrowski root-finding method
Grau, M
Díaz-Barrero, JL
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) : 450 - 456
[5] SOME 4TH ORDER MULTIPOINT ITERATIVE METHODS FOR EQUATIONS
JARRATT, P
[J]. MATHEMATICS OF COMPUTATION, 1966, 20 (95) : 434 - &
[6] FAMILY OF FOURTH ORDER METHODS FOR NONLINEAR EQUATIONS
KING, RF
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (05) : 876 - 879
[7] Some improvements of Ostrowski's method
Kou, Jisheng
Wang, Xiuhua
[J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (01) : 92 - 96
[8] KUNG HT, 1974, APPL MATH COMPUT, V21, P643
[9] Eighth-order methods with high efficiency index for solving nonlinear equations
Liu, Liping
Wang, Xia
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (09) : 3449 - 3454
[10] Ostrowski A.M., 1966, Solutions of Equations and Systems of Equations

← 1 2 →