Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

被引：21

作者：

Cordero, A. ^{[1
]}

Fardi, M. ^{[2
]}

Ghasemi, M. ^{[3
]}

Torregrosa, J. R. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46071 Valencia, Spain

[2] Islamic Azad Univ, Dept Math, Najafabad Branch, Najafabad, Iran

[3] Shahrekord Univ, Fac Math Sci, Dept Appl Math, Shahrekord, Iran

来源：

CALCOLO | 2014年 / 51卷 / 01期

关键词：

Convergence order; Efficiency index; Basin of attraction; Periodic orbit; Dynamical plane; Nonlinear equations; Iterative methods; MODIFIED OSTROWSKIS METHODS; OPTIMAL 8TH ORDER; CONVERGENCE; FAMILY; VARIANTS;

D O I：

10.1007/s10092-012-0073-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a family of optimal, in the sense of Kung-Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. We use the Ostrowski's efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods.

引用

页码：17 / 30

页数：14

共 13 条

[1] Three-step iterative methods with eighth-order convergence for solving nonlinear equations [J].

Bi, Weihong ;

Ren, Hongmin ;

Wu, Qingbiao .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) :105-112

[2] COMPLEX ANALYTIC DYNAMICS ON THE RIEMANN SPHERE [J].

BLANCHARD, P .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 11 (01) :85-141

[3] Some variants of King's fourth-order family of methods for nonlinear equations [J].

Chun, Changbum .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) :57-62

[4] Variants of Newton's Method using fifth-order quadrature formulas [J].

Cordero, A. ;

Torregrosa, Juan R. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) :686-698

[5] A family of modified Ostrowski's methods with optimal eighth order of convergence [J].

Cordero, Alicia ;

Torregrosa, Juan R. ;

Vassileva, Maria P. .

APPLIED MATHEMATICS LETTERS, 2011, 24 (12) :2082-2086

[6] New modifications of Potra-Ptaks method with optimal fourth and eighth orders of convergence [J].

Cordero, Alicia ;

Hueso, Jose L. ;

Martinez, Eulalia ;

Torregrosa, Juan R. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (10) :2969-2976

[7]

DOUADY A, 1985, ANN SCI ECOLE NORM S, V18, P287

[8] OPTIMAL ORDER OF ONE-POINT AND MULTIPOINT ITERATION [J].

KUNG, HT ;

TRAUB, JF .

JOURNAL OF THE ACM, 1974, 21 (04) :643-651

[9] Eighth-order methods with high efficiency index for solving nonlinear equations [J].

Liu, Liping ;

Wang, Xia .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (09) :3449-3454

[10]

Ostrowski A.M., 1966, Solutions of Equations and Systems of Equations

← 1 2 →