An optimal Steffensen-type family for solving nonlinear equations

被引：72
|
作者：
Zheng, Quan [1 ]
Li, Jingya [1 ]
Huang, Fengxi [1 ]
机构：
[1] N China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 23期
关键词：
Nonlinear equation; Newton's method; Steffensen's method; Derivative free; Optimal convergence;
D O I：
10.1016/j.amc.2011.04.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a general family of Steffensen-type methods with optimal order of convergence for solving nonlinear equations is constructed by using Newton's iteration for the direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub [H. T. Kung, J.F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Math. 21 (1974) 634-651] that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2(m-1). Its error equations and asymptotic convergence constants are obtained. Finally, it is compared with the related methods for solving nonlinear equations in the numerical examples. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：9592 / 9597
页数：6
相关论文
共 50 条
  • [1] Efficient Steffensen-type algorithms for solving nonlinear equations
    Argyros, I. K.
    Ren, Hongmin
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (03) : 691 - 704
  • [2] An efficient family of Steffensen-type methods with memory for solving systems of nonlinear equations
    Narang, Mona
    Bhatia, Saurabh
    Kanwar, Vinay
    COMPUTATIONAL AND MATHEMATICAL METHODS, 2021, 3 (06)
  • [3] Accelerated Steffensen-Type Methods for Solving Nonlinear Systems of Equations
    Cordero, Alicia
    Hueso, Jose L.
    Martinez, Eulalia
    Torregrosa, Juan R.
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
  • [4] A multistep Steffensen-type method for solving nonlinear systems of equations
    Amat, Sergio
    Argyros, Ioannis K.
    Busquier, Sonia
    Hernandez-Veron, Miguel A.
    Magrenan, A. Alberto
    Martinez, Eulalia
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (13) : 7518 - 7536
  • [5] SEMILOCAL CONVERGENCE OF STEFFENSEN-TYPE ALGORITHMS FOR SOLVING NONLINEAR EQUATIONS
    Ren, Hongmin
    Argyros, Ioannis K.
    Cho, Yeol Je
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2014, 35 (11) : 1476 - 1499
  • [6] EXTENDING THE APPLICABILITY OF EFFICIENT STEFFENSEN-TYPE ALGORITHMS FOR SOLVING NONLINEAR EQUATIONS
    Argyros, Ioannis K.
    George, Santhosh
    ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES, 2016, 15 (01): : 13 - 23
  • [7] Solving Nondifferentiable Nonlinear Equations by New Steffensen-Type Iterative Methods with Memory
    Jaiswal, J. P.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
  • [8] An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations
    Singh, Anuradha
    INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS, 2018, 9 (05) : 501 - 514
  • [9] A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations
    Eftekhari, Tahereh
    INTERNATIONAL JOURNAL OF ANALYSIS, 2014,
  • [10] A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEs
    Zheng, Quan
    Zhao, Peng
    Huang, Fengxi
    APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (21) : 8196 - 8203
12345