About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 318165, 14 pages
http://dx.doi.org/10.1155/2012/318165
Research Article

Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods

1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 21 August 2012; Accepted 20 September 2012

Academic Editor: Turgut Öziş

Copyright © 2012 F. Soleymani and S. Shateyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Iliev and N. Kyurkchiev, Nontrivial Methods in Numerical Analysis (Selected Topics in Numerical Analysis), Lambert Academy, 2010.
  2. B. H. Dayton, T.-Y. Li, and Z. Zeng, “Multiple zeros of nonlinear systems,” Mathematics of Computation, vol. 80, no. 276, pp. 2143–2168, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. F. Soleymani, M. Sharifi, and B. S. Mousavi, “An improvement of Ostrowski's and King's techniques with optimal convergence order eight,” Journal of Optimization Theory and Applications, vol. 153, no. 1, pp. 225–236, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, vol. 21, pp. 643–651, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. F. Steffensen, “Remarks on iteration,” Scandinavian Aktuarietidskr, vol. 16, pp. 64–72, 1933.
  6. F. Soleymani, “Two classes of iterative schemes for approximating simple roots,” Journal of Applied Sciences, vol. 11, no. 19, pp. 3442–3446, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Sharifi, D. K. R. Babajee, and F. Soleymani, “Finding the solution of nonlinear equations by a class of optimal methods,” Computers & Mathematics with Applications, vol. 63, no. 4, pp. 764–774, 2012. View at Publisher · View at Google Scholar
  8. F. Soleymani and S. Karimi Vanani, “Optimal Steffensen-type methods with eighth order of convergence,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4619–4626, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. F. Soleymani, S. K. Khattri, and S. Karimi Vanani, “Two new classes of optimal Jarratt-type fourth-order methods,” Applied Mathematics Letters, vol. 25, no. 5, pp. 847–853, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Q. Zheng, J. Li, and F. Huang, “An optimal Steffensen-type family for solving nonlinear equations,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9592–9597, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. K. Khattri and I. K. Argyros, “Sixth order derivative free family of iterative methods,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5500–5507, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A family of derivative-free methods with high order of convergence and its application to nonsmooth equations,” Abstract and Applied Analysis, vol. 2012, Article ID Article number836901, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. G. Alefeld, “Verified numerical computation for nonlinear equations,” Japan Journal of Industrial and Applied Mathematics, vol. 26, no. 2-3, pp. 297–315, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. M. Trott, The Mathematica Guidebook for Numerics, Springer, New York, NY, USA, 2006.
  15. http://www.mathematica.stackexchange.com/questions/5663/about-multi-root-search-inmathematica-for-transcendental-equations?lq=1.