How to Increase the Accessibility of Newton's Method for Operators With Center-Lipschitz Continuous First Derivative

被引：0
作者：
Ezquerro, J. A. [1 ]
Hernandez-Veron, M. A. [1 ]
Magrenan, A. A. [1 ]
机构：
[1] Univ La Rioja, Dept Math & Computat, Logrono, La Rioja, Spain
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2022年 / 43卷 / 03期
关键词：
the modified Newton method; Newton's method; hybrid method; semilocal convergence; majorizing sequence; accessibility; boundary value problem;
D O I：
10.1080/01630563.2022.2030352
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
As accessibility of Newton's method is very restrictive under a center-Lipschitz condition for the first derivative of the operator involved, we construct a hybrid iterative method to increase the accessibility of the method, where the modified Newton method is used to predict a good starting approximation for Newton's method. A boundary value problem illustrates this study.
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页码：350 / 363
页数：14
相关论文
共 14 条
  • [1] Argyros I.K., 1992, TAMKANG J MATH, V23, P269
  • [2] Weaker conditions for the convergence of Newton's method
    Argyros, Ioannis K.
    Hilout, Said
    [J]. JOURNAL OF COMPLEXITY, 2012, 28 (03) : 364 - 387
  • [3] How to improve the domain of parameters for Newton's method
    Ezquerro, J. A.
    Hernandez-Veron, M. A.
    [J]. APPLIED MATHEMATICS LETTERS, 2015, 48 : 91 - 101
  • [4] 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
  • [5] Ezquerro J. A., 2017, NEWTONS METHOD UPDAT
  • [6] Ezquerro J. A., 2020, MILD DIFFERENTIABILI
  • [7] FENYO I, 1954, ACTA MATH ACAD SCI H, V5, P85, DOI DOI 10.1007/BF02020389
  • [8] Newton's method under weak Kantorovich conditions
    Gutiérrez, JM
    Hernández, MA
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2000, 20 (04) : 521 - 532
  • [9] The Newton method for operators with Holder continuous first derivative
    Hernández, MA
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2001, 109 (03) : 631 - 648
  • [10] Kantorovich L. V., 2014, Functional Analysis
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