Fractal Newton Methods

被引:2
|
作者
Akgul, Ali [1 ,2 ,3 ]
Grow, David [4 ]
机构
[1] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut 11022801, Lebanon
[2] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkiye
[3] Near East Univ, Math Res Ctr, Dept Math, Near East Blvd, TR-99138 Nicosia, Turkiye
[4] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA
关键词
fractal derivative; fractal Newton methods; POLYNOMIALS; ROOTS;
D O I
10.3390/math11102277
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We introduce fractal Newton methods for solving f(x)=0 that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.
引用
收藏
页数:13
相关论文
共 50 条
  • [1] Fractal Newton basins
    Sahari, M. L.
    Djellit, I.
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2006, 2006
  • [2] CHAOTIC BEHAVIOUR IN NEWTON ITERATIVE PROCESS APPROACH - NEWTON'S FRACTAL
    Zlatic, Sanja
    TEHNICKI GLASNIK-TECHNICAL JOURNAL, 2013, 7 (04): : 347 - 354
  • [3] Approximate Newton Methods
    Ye, Haishan
    Luo, Luo
    Zhang, Zhihua
    JOURNAL OF MACHINE LEARNING RESEARCH, 2021, 22
  • [4] INEXACT NEWTON METHODS
    DEMBO, RS
    EISENSTAT, SC
    STEIHAUG, T
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (02) : 400 - 408
  • [5] Approximate Newton methods
    Ye, Haishan
    Luo, Luo
    Zhang, Zhihua
    Journal of Machine Learning Research, 2021, 22
  • [6] Multihomogeneous Newton methods
    Dedieu, JP
    Shub, M
    MATHEMATICS OF COMPUTATION, 2000, 69 (231) : 1071 - 1098
  • [7] Continuation Newton methods
    Axelsson, Owe
    Sysala, Stanislav
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (11) : 2621 - 2637
  • [9] From quasi-Newton methods to non-quasi-Newton methods
    袁亚湘
    ProgressinNaturalScience, 1997, (01) : 16 - 25
  • [10] On convergence domains of Newton's and modified newton methods
    Galpein, A
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (03) : 385 - 405