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Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains Cover

Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains

Open Access
|Jul 2019

References

  1. [1] Argyros I.K., On the Newton–Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004), 315–332.10.1016/j.cam.2004.01.029
  2. [2] Argyros I.K., Ezquerro J.A., Gutiérrez J.M., Hernández M.A., Hilout S., On the semilocal convergence of efficient Chebyshev-Secant-type methods, J. Comput. Appl. Math. 235 (2011), 3195–3206.10.1016/j.cam.2011.01.005
  3. [3] Argyros I.K., Ren H., Efficient Steffensen-type algorithms for solving nonlinear equations, Int. J. Comput. Math. 90 (2013), 691–704.10.1080/00207160.2012.737461
  4. [4] Argyros I.K., Computational Theory of Iterative Methods, Studies in Computational Mathematics, 15, Elsevier B.V., New York, 2007.
  5. [5] Ezquerro J.A., Hernández M.A., An optimization of Chebyshev’s method, J. Complexity 25 (2009), 343–361.10.1016/j.jco.2009.04.001
  6. [6] Ezquerro J.A., Grau A., Grau-Sánchez M., Hernández M.A., Construction of derivative-free iterative methods from Chebyshev’s method, Anal. Appl. (Singap.) 11 (2013), 1350009, 16 pp.10.1142/S0219530513500097
  7. [7] Ezquerro J.A., Gutiérrez J.M., Hernández M.A., Salanova M.A., Chebyshev-like methods and quadratic equations, Rev. Anal. Numér. Théor. Approx. 28 (1999), 23–35.
  8. [8] Grau M., Díaz-Barrero J.L., An improvement of the Euler–Chebyshev iterative method, J. Math. Anal. Appl. 315 (2006), 1–7.10.1016/j.jmaa.2005.09.086
  9. [9] Grau-Sánchez M., Gutiérrez J.M., Some variants of the Chebyshev–Halley family of methods with fifth order of convergence, Int. J. Comput. Math. 87 (2010), 818–833.10.1080/00207160802208358
  10. [10] Hueso J.L., Martinez E., Teruel C., Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems, J. Comput. Appl. Math. 275 (2015), 412–420.10.1016/j.cam.2014.06.010
  11. [11] Magreñán Á.A., Estudio de la dinámica del método de Newton amortiguado, PhD Thesis, Universidad de La Rioja, Servicio de Publicaciones, Logroño, 2013. Available at http://dialnet.unirioja.es/servlet/tesis?codigo=38821
  12. [12] Magreñán Á.A., Different anomalies in a Jarratt family of iterative root-finding methods, Appl. Math. Comput. 233 (2014), 29–38.10.1016/j.amc.2014.01.037
  13. [13] Magreñán Á.A., A new tool to study real dynamics: the convergence plane, Appl. Math. Comput. 248 (2014), 215–224.10.1016/j.amc.2014.09.061
  14. [14] Prashanth M., Mosta S.S., Gupta D.K., Semi-local convergence of the Supper-Halley’s method under w-continuous second derivative in Banach space. Submitted.
  15. [15] Rheinboldt W.C., An adaptive continuation process for solving systems of nonlinear equations, in: Tikhonov A.N., et al. (eds.), Mathematical Models and Numerical Methods, Banach Center Publ., 3, PWN, Warsaw, 1978, pp. 129–142.10.4064/-3-1-129-142
  16. [16] Traub J.F., Iterative Methods for the Solution of Equations, Prentice-Hall Series in Automatic Computation, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1964.
DOI: https://doi.org/10.2478/amsil-2018-0008 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 21 - 40
Submitted on: Oct 9, 2017
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Accepted on: Aug 25, 2018
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Published on: Jul 18, 2019
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2019 Ioannis K. Argyros, Santhosh George, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.