A modified Newton-type method with sixth-order convergence for solving nonlinear equations

被引：1
作者：
Fang, Liang [1 ]
Chen, Tao [1 ]
Tian, Li [1 ]
Sun, Li [1 ]
Chen, Bin [2 ]
机构：
[1] Taishan Univ, Coll Math & Syst Sci, Tai An 271021, Shandong, Peoples R China
[2] Taishan Expt Midlle Sch, Math Educ Res Group, Tai An 271000, Shandong, Peoples R China
来源：
CEIS 2011 | 2011年 / 15卷
关键词：
Newton-type method; Nonlinear equations; Order of convergence; Iterative method; Efficiency index;
D O I：
10.1016/j.proeng.2011.08.586
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we present and analyze a sixth-order convergent iterative method for solving nonlinear equations. The method is free from second derivatives and permits f'(x) = 0 in iteration points. Some numerical examples illustrate that the presented method is more efficient and performs better than classical Newton's method. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011]
引用
收藏
页数：5
相关论文
共 11 条
  • [1] Some variants of King's fourth-order family of methods for nonlinear equations
    Chun, Changbum
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) : 57 - 62
  • [2] A cubically convergent Newton-type method under weak conditions
    Fang, Liang
    He, Guoping
    Hu, Zhongyong
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) : 409 - 412
  • [3] Some modified Newton-type methods with order of convergence varied from two to six under weak conditions
    Fang, Liang
    He, Guoping
    Hu, Yunhong
    Sun, Li
    [J]. INTERNATIONAL JOINT CONFERENCE ON COMPUTATIONAL SCIENCES AND OPTIMIZATION, VOL 2, PROCEEDINGS, 2009, : 637 - +
  • [4] Some modifications of Newton's method with higher-order convergence for solving nonlinear equations
    Fang, Liang
    He, Guoping
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 228 (01) : 296 - 303
  • [5] Fang L, 2008, COMPUT APPL MATH, V27, P269, DOI 10.1590/S1807-03022008000300003
  • [6] An improvement to Ostrowski root-finding method
    Grau, M
    Díaz-Barrero, JL
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) : 450 - 456
  • [7] The improvements of modified Newton's method
    Kou, Jisheng
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (01) : 602 - 609
  • [8] Fifth-order iterative methods for solving nonlinear equations
    Noor, Muhammad Aslam
    Noor, Khalida Inayat
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) : 406 - 410
  • [9] Modified iterative methods with cubic convergence for solving nonlinear equations
    Noor, Muhammad Aslam
    Noor, Khalida Inayat
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 184 (02) : 322 - 325
  • [10] Fourth-order convergent iterative method for nonlinear equation
    Noor, Muhammad Aslam
    Ahmad, Faizan
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (02) : 1149 - 1153
12