A note on some quadrature based three-step iterative methods for non-linear equations

被引：6

作者：

Ding, Heng-fei ^{[2
]}

Zhang, Yu-xin ^{[1
]}

Wang, San-fu ^{[2
]}

Yang, Xiao-ya ^{[2
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 01期

关键词：

Non-linear equations; Three-step iterative methods; Efficiency index; Order of convergence; Numerical examples; VARIANTS; FAMILY;

D O I：

10.1016/j.amc.2009.04.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a recent paper [N. A. Mir, T. Zaman, Some quadrature based three-step iterative methods for non-linear equations, Appl. Math. Comput. 193 (2007) 366-373], some new three-step iterative methods for non-linear equations have been proposed. In this note, we show that the Algorithm 2.2 and Algorithm 2.3 given by the authors have twelfth-order and ninth-order convergence respectively, not seventh-order one as claimed in their work. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：53 / 57

页数：5

共 12 条

[1]

BI W, 2008, J COMPUT APPL MATH, V209

[2] New family of seventh-order methods for nonlinear equations [J].

Bi, Weihong ;

Ren, Hongmin ;

Wu, Qingbiao .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 203 (01) :408-412

[3] A note on modified Householder iterative method free from second derivatives for nonlinear equations [J].

Chen, Bilian ;

Ma, Changfeng .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 203 (02) :913-915

[4] Some sixth-order variants of Ostrowski root-finding methods [J].

Chun, Changbum ;

Ham, YoonMee .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (02) :389-394

[5] Some fourth-order iterative methods for solving nonlinear equations [J].

Chun, Changbum .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 195 (02) :454-459

[6] A family of combined iterative methods for solving nonlinear equation [J].

Han, Danfu ;

Wu, Peng .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 195 (02) :448-453

[7] Some variants of Ostrowski's method with seventh-order convergence [J].

Kou, Jisheng ;

Li, Yitian ;

Wang, Xiuhua .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 209 (02) :153-159

[8] Some quadrature based three-step iterative methods for non-linear equations [J].

Mir, Nazir Ahmad ;

Zaman, Tooba .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (02) :366-373

[9] Iterative methods with fourth-order convergence for nonlinear equations [J].

Noor, Khalida Inayat ;

Noor, Muhammad Aslam .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (01) :221-227

[10] A sixth order method for nonlinear equations [J].

Parhi, S. K. ;

Gupta, D. K. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 203 (01) :50-55

← 1 2 →