A family of modified Ostrowski's methods with optimal eighth order of convergence

被引：26

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：

APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 12期

关键词：

Nonlinear equations; Iterative methods; Convergence order; Efficiency index;

D O I：

10.1016/j.aml.2011.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. 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 are optimal according to the Kung and Traub's conjecture (1974) [2]. Numerical comparisons are made to show the performance of the derived method, as is shown in the numerical section. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2082 / 2086

页数：5

共 50 条

[31] On the new family of optimal eighth order methods developed by Lotfi et al.
Changbum Chun
Beny Neta
Numerical Algorithms, 2016, 72 : 363 - 376
[32] A new optimal eighth-order family of iterative methods for the solution of nonlinear equations
Chun, Changbum
Lee, Mi Young
APPLIED MATHEMATICS AND COMPUTATION, 2013, 223 : 506 - 519
[33] On the new family of optimal eighth order methods developed by Lotfi et al.
Chun, Changbum
Neta, Beny
NUMERICAL ALGORITHMS, 2016, 72 (02) : 363 - 376
[34] An Optimal Family of Eighth-Order Methods for Multiple-Roots and Their Complex Dynamics
Kumar, Sunil
Sharma, Janak Raj
Jantschi, Lorentz
SYMMETRY-BASEL, 2024, 16 (08):
[35] On the convergence of an optimal fourth-order family of methods and its dynamics
Argyros, Ioannis K.
Alberto Magrenan, A.
APPLIED MATHEMATICS AND COMPUTATION, 2015, 252 : 336 - 346
[36] Comparison of several families of optimal eighth order methods
Chun, Changbum
Neta, Beny
APPLIED MATHEMATICS AND COMPUTATION, 2016, 274 : 762 - 773
[37] Fourth-Order Derivative-Free Optimal Families of King's and Ostrowski's Methods
Behl, Ramandeep
Motsa, S. S.
Kansal, Munish
Kanwar, V.
MATHEMATICAL ANALYSIS AND ITS APPLICATIONS, 2015, 143 : 359 - 371
[38] Regarding the accuracy of optimal eighth-order methods
Soleymani, F.
MATHEMATICAL AND COMPUTER MODELLING, 2011, 53 (5-6) : 1351 - 1357
[39] Some novel and optimal families of King's method with eighth and sixteenth-order of convergence
Maroju, P.
Behl, Ramandeep
Motsa, S. S.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 318 : 136 - 148
[40] New modifications of Hansen-Patrick's family with optimal fourth and eighth orders of convergence
Kansal, Munish
Kanwar, V.
Bhatia, Saurabh
APPLIED MATHEMATICS AND COMPUTATION, 2015, 269 : 507 - 519

← 1 2 3 4 5 →