An Efficient Derivative-Free Method for the Solution of Systems of Equations

被引：6
作者：
Chun, Changbum [1 ]
Neta, Beny [2 ]
机构：
[1] Sungkyunkwan Univ, Dept Math, Suwon, South Korea
[2] Naval Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2021年 / 42卷 / 07期
基金：
新加坡国家研究基金会;
关键词：
Derivative free methods; divided differences; iterative method; Steffensen's method; systems of nonlinear equations; SOLVING SYSTEMS; ITERATIVE METHODS; ORDER; CONVERGENCE; FAMILY; MEMORY; 4TH;
D O I：
10.1080/01630563.2021.1931313
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We have modified our previously developed fourth order method to approximate solution of systems of equations including non-differentiable ones. The most recent article by Kumar et al. (Numer. Algor. 86:1051-1070, 2021) compared fourth order and seventh order methods to show the efficiency of their fourth order. We have shown that our method compares favorably with methods in the literature.
引用
收藏
页码：834 / 848
页数：15
相关论文
共 24 条
  • [1] New efficient methods for solving nonlinear systems of equations with arbitrary even order
    Abbasbandy, Saeid
    Bakhtiari, Parisa
    Cordero, Alicia
    Torregrosa, Juan R.
    Lotfi, Taher
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2016, 287 : 94 - 103
  • [2] Amat S, 2016, SEMA SIMAI SPRING S, V10, P1, DOI 10.1007/978-3-319-39228-8
  • [3] [Anonymous], 1981, APPROX THEORY APPL
  • [4] Design and multidimensional extension of iterative methods for solving nonlinear problems
    Artidiello, S.
    Cordero, Alicia
    Torregrosa, Juan R.
    Vassileva, M. P.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 : 194 - 203
  • [5] Stable high-order iterative methods for solving nonlinear models
    Behl, Ramandeep
    Cordero, Alicia
    Motsa, Sandile S.
    Torregrosa, Juan R.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 303 : 70 - 88
  • [6] Developing high order methods for the solution of systems of nonlinear equations
    Chun, Changbum
    Neta, Beny
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 342 : 178 - 190
  • [7] Iterative Methods with Memory for Solving Systems of Nonlinear Equations Using a Second Order Approximation
    Cordero, Alicia
    Maimo, Javier G.
    Torregrosa, Juan R.
    Vassileva, Maria P.
    [J]. MATHEMATICS, 2019, 7 (11)
  • [8] Increasing the convergence order of an iterative method for nonlinear systems
    Cordero, Alicia
    Hueso, Jose L.
    Martinez, Eulalia
    Torregrosa, Juan R.
    [J]. APPLIED MATHEMATICS LETTERS, 2012, 25 (12) : 2369 - 2374
  • [9] On Steffensen's method on Banach spaces
    Ezquerro, J. A.
    Hernandez, M. A.
    Romero, N.
    Velasco, A. I.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 249 : 9 - 23
  • [10] Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems
    Hueso, Jose L.
    Martinez, Eulalia
    Teruel, Caries
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 275 : 412 - 420
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