A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces

被引:1
|
作者
Sharma, Janak Raj [1 ]
Singh, Harmandeep [1 ]
Argyros, Ioannis K. [2 ]
机构
[1] St Longowal Inst Engn & Technol, Dept Math, Longowal 148106, Punjab, India
[2] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
关键词
convergence analysis; iterative methods; Frechet-derivative; Banach spaces;
D O I
10.3390/math10173196
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve the computation of derivatives of an order higher than one. However, the convergence analysis was carried out in earlier studies by using the assumptions on the higher order derivatives as well. Such types of assumptions limit the applicability of techniques. In this regard, the convergence analysis is developed in the present study by imposing the conditions on first order derivatives only. The central idea for the local analysis is to estimate the bounds on convergence domain as well as the error approximations of the iterates along with the formulation of sufficient conditions for the uniqueness of the solution. Based on the choice of initial estimate in the given domain, the semilocal analysis is established, which ensures the convergence of iterates to a unique solution in that domain. Further, some applied problems are tested to certify the theoretical deductions.
引用
收藏
页数:16
相关论文
共 50 条
  • [21] Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces
    Sukhjit Singh
    D. K. Gupta
    E. Martínez
    José L. Hueso
    Mediterranean Journal of Mathematics, 2016, 13 : 4219 - 4235
  • [22] Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces
    Singh, Sukhjit
    Gupta, D. K.
    Martinez, E.
    Hueso, Jose L.
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (06) : 4219 - 4235
  • [23] Higher order Traub-Steffensen type methods and their convergence analysis in Banach spaces
    Kumar, Deepak
    Sharma, Janak Raj
    Singh, Harmandeep
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2023, 24 (04) : 1565 - 1587
  • [24] Semilocal convergence of a sixth-order Jarratt method in Banach spaces
    Wang, Xiuhua
    Kou, Jisheng
    Gu, Chuanqing
    NUMERICAL ALGORITHMS, 2011, 57 (04) : 441 - 456
  • [25] Semilocal convergence of a sixth-order Jarratt method in Banach spaces
    Xiuhua Wang
    Jisheng Kou
    Chuanqing Gu
    Numerical Algorithms, 2011, 57 : 441 - 456
  • [26] Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces
    Kumar, Deepak
    Kumar, Sunil
    Sharma, Janak Raj
    Jantschi, Lorentz
    MATHEMATICS, 2021, 9 (19)
  • [27] Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces
    Zheng, Lin
    Gu, Chuanqing
    NUMERICAL ALGORITHMS, 2012, 59 (04) : 623 - 638
  • [28] Semilocal Convergence Of Sixth Order Method By Using Recurrence Relations In Banach Spaces
    Madhu, Kalyanasundaram
    APPLIED MATHEMATICS E-NOTES, 2018, 18 : 197 - 208
  • [29] Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces
    Lin Zheng
    Chuanqing Gu
    Numerical Algorithms, 2012, 59 : 623 - 638
  • [30] Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces
    Wang, Xiuhua
    Kou, Jisheng
    Gu, Chuanqing
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 153 (03) : 779 - 793