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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 497023, 24 pages
Construction of Optimal Derivative-Free Techniques without Memory
1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Allied Network for Policy Research and Advocacy for Sustainability, IEEE, Mauritius, Mauritius
3Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
4School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, South Africa
Received 5 July 2012; Accepted 3 September 2012
Academic Editor: Alicia Cordero
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.
- J. F. Steffensen, “Remarks on iteration,” Skand Aktuar Tidsr, vol. 16, pp. 64–72, 1933.
- 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.
- 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.
- T. Sauer, Numerical Analysis, Pearson, Boston, Mass, USA, 2006.
- 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.
- F. Soleymani, “On a bi-parametric class of optimal eighth-order derivative-free methods,” International Journal of Pure and Applied Mathematics, vol. 72, no. 1, pp. 27–37, 2011.
- 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.
- 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.
- D. K. R. Babajee, Analysis of higher order variants of Newton’s method and their applications to differential and integral equations and in ocean acidification [Ph.D. thesis], University of Mauritius, 2010.
- Z. Liu, Q. Zheng, and P. Zhao, “A variant of Steffensen's method of fourth-order convergence and its applications,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 1978–1983, 2010.
- A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “Steffensen type methods for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 236, no. 12, pp. 3058–3064, 2012.
- F. Soleymani, “An optimally convergent three-step class of derivative-free methods,” World Applied Sciences Journal, vol. 13, no. 12, pp. 2515–2521, 2011.
- M. S. Petković, S. Ilić, and J. Džunić, “Derivative free two-point methods with and without memory for solving nonlinear equations,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 1887–1895, 2010.
- 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.
- J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, New York, NY, USA, 1982.
- F. Soleymani, “Optimized Steffensen-type methods with eighth order of convergence and high efficiency index,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 932420, 18 pages, 2012.
- F. Soleymani, D. K. R. Babajee, and M. Sharifi, “Modified Jarratt method without memory with twelfth-order convergence,” Annals of the University of Craiova, vol. 39, pp. 21–34, 2012.
- F. Soleymani, “On a new class of optimal eighth-order derivative-free methods,” Acta Universitatis Sapientiae. Mathematica, vol. 3, pp. 169–180, 2011.
- F. Soleymani and F. Soleimani, “Novel computational derivative-free methods for simple roots,” Fixed Point Theory, vol. 13, no. 1, pp. 247–258, 2012.
- H. Ren, Q. Wu, and W. Bi, “A class of two-step Steffensen type methods with fourth-order convergence,” Applied Mathematics and Computation, vol. 209, no. 2, pp. 206–210, 2009.
- A. Cordero, J. L. Hueso, E. Martinez, and J. R. Torregrosa, “Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation,” Mathematical and Computer Modelling. In press.
- F. Soleymani, “Two classes of iterative schemes for approximating simple roots,” Journal of Applied Sciences, vol. 11, no. 19, pp. 3442–3446, 2011.
- R. Hazrat, Mathematica: A Problem-Centered Approach, Springer, New York, NY, USA, 2010.
- J. Hoste, Mathematica Demystified, McGraw-Hill, New York, NY, USA, 2009.