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Ball convergence for Traub-Steffensen like methods in Banach space Cover

Ball convergence for Traub-Steffensen like methods in Banach space

Annals of West University of Timisoara - Mathematics and Computer Science
Volume 53 (2015): Issue 2 (December 2015)
By: Ioannis K. Argyros and  Santhosh George  
Open Access
|Apr 2016

References

  1. [1] M. F. Abad, A. Cordero, and J. R. Torregrosa, Fourth and Fifth-order methods for solving nonlinear systems of equations: An application to the global positioning system, Abstract and Applied Analysis, (2013), Article ID 58670810.1155/2013/586708
    Search in Google Scholar
  2. [2] S. Amat, M.A. Hernández, and N. Romero, Semilocal convergence of a sixth order iterative method for quadratic equations, Applied Numerical Mathematics, 62, (2012), 833-84110.1016/j.apnum.2012.03.001
    Search in Google Scholar
  3. [3] I.K. Argyros, Computational theory of iterative methods, Elsevier Publ. Co. New York, U.S.A, 15, 2007
    Search in Google Scholar
  4. [4] I.K. Argyros, A semilocal convergence analysis for directional Newton methods, Math. Comput.80, (2011), 327–34310.1090/S0025-5718-2010-02398-1
    Search in Google Scholar
  5. [5] I.K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton’s method, J. Complexity, 28, (2012), 364–38710.1016/j.jco.2011.12.003
    Search in Google Scholar
  6. [6] I. K. Argyros and S. Hilout, Computational methods in nonlinear analysis. Efficient algorithms, fixed point theory and applications, World Scientific, 201310.1142/8475
    Search in Google Scholar
  7. [7] I.K. Aryros and H. Ren, Improved local analysis for certain class of iterative methods with cubic convergence, Numerical Algorithms, 59, (2012), 505-52110.1007/s11075-011-9501-6
    Search in Google Scholar
  8. [8] V. Candela and A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing, 45 (4), (1990), 355-367
    Search in Google Scholar
  9. [9] A. Cordero, J. R. Torregrosa, and M. P. Vasileva, Increasing the order of convergence of iterative schemes for solving nonlinear systems, J. Comput. Appl. Math.252, (2013), 86–9410.1016/j.cam.2012.11.024
    Search in Google Scholar
  10. [10] J. M. Gutiérrez, A.A. Magreñán, and N. Romero, On the semi-local convergence of Newton-Kantorovich method under center-Lipschitz conditions, Applied Mathematics and Computation, 221, (2013), 79-8810.1016/j.amc.2013.05.078
    Search in Google Scholar
  11. [11] M.A. Hernández and M.A. Salanova, Modification of the Kantorovich assumptions for semi-local convergence of the Chebyshev method, Journal of Computational and Applied Mathematics, 126, (2000), 131-14310.1016/S0377-0427(99)00347-7
    Search in Google Scholar
  12. [12] L.V. Kantorovich and G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982
    Search in Google Scholar
  13. [13] J.S. Kou, Y. T. Li, and X.H. Wang, A modification of Newton method with third-order convergence, Appl. Math. Comput.181, (2006), 1106-111110.1016/j.amc.2006.01.076
    Search in Google Scholar
  14. [14] A. A. Magrenan, Different anomalies in a Jarratt family of iterative root finding methods, Appl. Math. Comput.233, (2014), 29-3810.1016/j.amc.2014.01.037
    Search in Google Scholar
  15. [15] A. A. Magrenan, A new tool to study real dynamics: The convergence plane, Appl. Math. Comput.248, (2014), 29-3810.1016/j.amc.2014.09.061
    Search in Google Scholar
  16. [16] M. S. Petkovic, B. Neta, L. Petkovic, and J. Džunič, Multipoint methods for solving nonlinear equations, Elsevier, 2013
    Search in Google Scholar
  17. [17] F. A. Potra and V. Pták, Nondiscrete Induction and Iterative Processes, Pitman, Boston, 103, 1984
    Search in Google Scholar
  18. [18] H. Ren and Q. Wu, Convergence ball and error analysis of a family of iterative methods with cubic convergence, Appl. Math. Comput.209, (2009), 369-37810.1016/j.amc.2008.12.057
    Search in Google Scholar
  19. [19] W.C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, Banach Center, Warsaw, Poland, 3, 197710.4064/-3-1-129-142
    Search in Google Scholar
  20. [20] J.R. Sharma, P.K. Guha, and R. Sharma, An efficient fourth order weighted-Newton method for systems of nonlinear equations, Numerical Algorithms, 62 (2), (2013), 307-32310.1007/s11075-012-9585-7
    Search in Google Scholar
  21. [21] F. Soleymani, T. Lofti, and P. Bakhtiari, A multi-step class of iterative methods for nonlinear systems, Optim. Lett.8, (2014), 1001–101510.1007/s11590-013-0617-6
    Search in Google Scholar
  22. [22] J.F.Traub, Iterative methods for the solution of equations, AMS Chelsea Publishing, 1982
    Search in Google Scholar
  23. [23] S. Weerakoon and T.G.I. Fernando, A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett.13, (2000), 87-9310.1016/S0893-9659(00)00100-2
    Search in Google Scholar
DOI: https://doi.org/10.1515/awutm-2015-0011 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
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Language: English
Page range: 3 - 16
Submitted on: Apr 30, 2015
Accepted on: Jan 27, 2016
Published on: Apr 9, 2016
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
Steffensen method,
Traub-Steffensen method,
Banach space,
Fréchet derivative,
local convergence,
third order of convergence
Related subjects:
Mathematics,
General mathematics

© 2016 Ioannis K. Argyros, Santhosh George, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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