On a sixth-order Jarratt-type method in Banach spaces

被引：1
|
作者：
Argyros, Ioannis K. [1 ]
George, Santhosh [2 ]
机构：
[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
[2] NIT, Dept Math & Computat Sci, Mangalore 575025, Karnataka, India
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2015年 / 8卷 / 04期
关键词：
Jarratt-type methods; Banach space; local convergence; Frechet-derivative;
D O I：
10.1142/S1793557115500655
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a local convergence analysis of a sixth-order Jarratt-type method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Frechet-derivative of the operator involved. Earlier studies such as [X. Wang, J. Kou and C. Gu, Semilocal convergence of a sixth-order Jarratt method in Banach spaces, Numer. Algorithms 57 (2011) 441456.] require hypotheses up to the third Frechet-derivative. Numerical examples are also provided in this study.
引用
收藏
页数：12
相关论文
共 50 条
  • [31] A sixth-order optimal collocation method for elliptic problems
    Bum Il Hong
    Sung Nam Ha
    Nahmwoo Hahm
    Korean Journal of Computational & Applied Mathematics, 1999, 6 (2): : 411 - 420
  • [32] A variant of Chebyshev's method with sixth-order convergence
    Kou, Jisheng
    Li, Yitian
    NUMERICAL ALGORITHMS, 2006, 43 (03) : 273 - 278
  • [33] A variant of Chebyshev’s method with sixth-order convergence
    Jisheng Kou
    Yitian Li
    Numerical Algorithms, 2006, 43 : 273 - 278
  • [34] A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations
    Eftekhari, Tahereh
    INTERNATIONAL JOURNAL OF ANALYSIS, 2014,
  • [35] Development of a Family of Jarratt-Like Sixth-Order Iterative Methods for Solving Nonlinear Systems with Their Basins of Attraction
    Lee, Min-Young
    Kim, Young Ik
    ALGORITHMS, 2020, 13 (11)
  • [36] A Modified Newton-Type Method with Sixth-Order Convergence for Solving Nonlinear Equations
    Sun, Li
    Fang, Liang
    ADVANCES IN COMPUTER SCIENCE, ENVIRONMENT, ECOINFORMATICS, AND EDUCATION, PT IV, 2011, 217 : 470 - +
  • [37] An Efficient Sixth-Order Convergent Newton-type Iterative Method for Nonlinear Equations
    Hu, Zhongyong
    Fang, Liang
    Li, Lianzhong
    Chen, Rui
    ADVANCES IN MANUFACTURING TECHNOLOGY, PTS 1-4, 2012, 220-223 : 2585 - 2588
  • [38] A Modification of Newton-type Method with Sixth-order Convergence for Solving Nonlinear Equations
    Chen, Rui
    Fang, Liang
    MECHATRONICS AND INTELLIGENT MATERIALS II, PTS 1-6, 2012, 490-495 : 1839 - 1843
  • [39] A modified Newton-type method with sixth-order convergence for solving nonlinear equations
    Fang, Liang
    Chen, Tao
    Tian, Li
    Sun, Li
    Chen, Bin
    CEIS 2011, 2011, 15
  • [40] Local convergence analysis of jarratt-type schemes for solving equations
    Argyros I.K.
    George S.
    Applied Set-Valued Analysis and Optimization, 2019, 1 (01): : 53 - 62
12345