Improved convergence analysis for the secant method based on a certain type of recurrence relations

被引：5
|
作者：
Argyros, IK [1 ]
机构：
[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2004年 / 81卷 / 05期
关键词：
secant method; Banach space; divided difference of order one; Frechet-derivative; semilocal/local convergence;
D O I：
10.1080/00207160410001688600
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide new sufficient conditions for the local as well as semilocal convergence of the secant method in a Banach space. Using a certain type of recurrence relations, we provide a finer convergence analysis than before. Moreover, our conditions compare favourably with earlier ones, which allow us to apply our results in cases not covered before.
引用
收藏
页码：629 / 637
页数：9
相关论文
共 50 条
  • [21] A New Semi-local Convergence Analysis of the Secant Method
    Argyros I.K.
    Uko L.U.
    Nathanson E.
    International Journal of Applied and Computational Mathematics, 2017, 3 (Suppl 1) : 225 - 232
  • [22] EXTENDED CONVERGENCE OF A TWO-STEP-SECANT-TYPE METHOD UNDER A RESTRICTED CONVERGENCE DOMAIN
    Argyros, Ioannis K.
    George, Santhosh
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2021, 45 (01): : 155 - 164
  • [23] Convergence and dynamics of improved Chebyshev-Secant-type methods for non differentiable operators
    Abhimanyua Kumar
    D. K. Gupta
    Eulalia Martínez
    José L. Hueso
    Numerical Algorithms, 2021, 86 : 1051 - 1070
  • [24] Convergence and dynamics of improved Chebyshev-Secant-type methods for non differentiable operators
    Kumar, Abhimanyua
    Gupta, D. K.
    Martinez, Eulalia
    Hueso, Jose L.
    NUMERICAL ALGORITHMS, 2021, 86 (03) : 1051 - 1070
  • [25] IMPROVED CONVERGENCE ANALYSIS OF MIXED SECANT METHODS FOR PERTURBED SUBANALYTIC VARIATIONAL INCLUSIONS
    Argyros, Ioannis K.
    Gonzalez, Daniel
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2016,
  • [26] ON AN IMPROVED UNIFIED CONVERGENCE ANALYSIS FOR A CERTAIN CLASS OF EULER-HALLEY TYPE METHODS
    Argyros, Ioannis K.
    JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2006, 13 (03): : 207 - 215
  • [27] The convergence ball and error analysis of the two-step Secant method
    LIN Rong-fei
    WU Qing-biao
    CHEN Min-hong
    KHAN Yasir
    LIU Lu
    AppliedMathematics:AJournalofChineseUniversities, 2017, 32 (04) : 397 - 406
  • [28] The convergence ball and error analysis of the two-step Secant method
    Rong-fei Lin
    Qing-biao Wu
    Min-hong Chen
    Yasir Khan
    Lu Liu
    Applied Mathematics-A Journal of Chinese Universities, 2017, 32 : 397 - 406
  • [29] The convergence ball and error analysis of the two-step Secant method
    Lin, Rong-fei
    Wu, Qing-biao
    Chen, Min-hong
    Khan, Yasir
    Liu, Lu
    APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2017, 32 (04) : 397 - 406
  • [30] An Improved Error Analysis for the Secant Method Under the Gamma Condition
    Argyros, Ioannis K.
    PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2007, 39 : 1 - 11
12345