Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 958020, 13 pages
http://dx.doi.org/10.1155/2012/958020
Research Article

Computing Simple Roots by an Optimal Sixteenth-Order Class

1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
3Department of Civil Engineering, Islamic Azad University, Zahedan Branch, Zahedan, Iran

Received 21 August 2012; Revised 6 October 2012; Accepted 7 October 2012

Academic Editor: Changbum Chun

Copyright © 2012 F. Soleymani et al. 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. T. Sauer, Numerical Analysis, Pearson, Boston, Mass, USA, 2nd edition, 2011. View at Zentralblatt MATH
  2. F. Soleymani, “Optimized Steffensen-type methods with eighth-order convergence and high efficiency index,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 932420, 18 pages, 2012. View at Google Scholar
  3. M. Heydari, S. M. Hosseini, and G. B. Loghmani, “Convergence of a family of third-order methods free from second derivatives for finding multiple roots of nonlinear equations,” World Applied Sciences Journal, vol. 11, pp. 507–512, 2010. View at Google Scholar
  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. F. Soleymani, “Optimal fourth-order iterative methods free from derivatives,” Miskolc Mathematical Notes, vol. 12, no. 2, pp. 255–264, 2011. View at Google Scholar
  6. F. Soleymani, R. Sharma, X. Li, and E. Tohidi, “An optimized derivative-free form of the Potra-Ptak method,” Mathematical and Computer Modelling, vol. 56, pp. 97–104, 2012. View at Publisher · View at Google Scholar
  7. F. Soleymani and B. S. Mousavi, “On novel classes of iterative methods for solving nonlinear equations,” Computational Mathematics and Mathematical Physics, vol. 52, no. 2, pp. 214–221, 2012. View at Publisher · View at Google Scholar
  8. B. Neta and M. S. Petković, “Construction of optimal order nonlinear solvers using inverse interpolation,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2448–2455, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Y. H. Geum and Y. I. Kim, “A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3278–3287, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. 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
  11. X. Wang and L. Liu, “New eighth-order iterative methods for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 234, no. 5, pp. 1611–1620, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. S. Wolfram, The Mathematica Book, Wolfram Media, 5th edition, 2003.
  13. J. R. Sharma and R. Sharma, “A new family of modified Ostrowski's methods with accelerated eighth order convergence,” Numerical Algorithms, vol. 54, no. 4, pp. 445–458, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. H. Geum and Y. I. Kim, “A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function,” Journal of Computational and Applied Mathematics, vol. 235, no. 10, pp. 3178–3188, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. H. Geum and Y. I. Kim, “A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1336–1342, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. H. Montazeri, F. Soleymani, S. Shateyi, and S. S. Motsa, “On a new method for computing the numerical solution of systems of nonlinear equations,” Journal of Applied Mathematics, vol. 2012, Article ID 751975, 15 pages, 2012. View at Google Scholar
  17. Y. I. Kim and C. Chun, “New twelfth-order modifications of Jarratt’s method for solving nonlinear equations,” Studies in Nonlinear Sciences, vol. 1, pp. 14–18, 2010. View at Google Scholar
  18. Y. I. Kim, C. Chun, and W. Kim, “Some third-order curvature based methods for solving nonlinear equations,” Studies in Nonlinear Sciences, vol. 1, pp. 72–76, 2010. View at Google Scholar
  19. F. Soleymani and S. K. Khattri, “Finding simple roots by seventh- and eighth-order derivative-free methods,” International Journal of Mathematical Models and Methods in Applied Sciences, vol. 6, pp. 45–52, 2012. View at Google Scholar
  20. F. Soleymani, “Optimal eighth-order simple root-finders free from derivative,” WSEAS Transactions on Information Science and Applications, vol. 8, pp. 293–299, 2011. View at Google Scholar
  21. F. Soleymani and F. Soleimani, “Novel computational derivative-free methods for simple roots,” Fixed Point Theory, vol. 13, no. 1, pp. 247–258, 2012. View at Google Scholar
  22. J. B. Keiper, “Interval arithmetic in mathematica,” The Mathematica Journal, vol. 5, pp. 66–71, 1995. View at Google Scholar