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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 836901, 15 pages
A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations
Instituto de Matemática Multidisciplinar and Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Received 4 January 2012; Accepted 14 March 2012
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Alicia Cordero 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. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970.
- A. M. Ostrowski, Solution of Equations and Systems of Equations, Pure and Applied Mathematics, Vol. 9, Academic Press, New York, NY, USA, 1966.
- 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.
- 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.
- M. Dehghan and M. Hajarian, “Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations,” Computational & Applied Mathematics, vol. 29, no. 1, pp. 19–30, 2010.
- A. Cordero and J. R. Torregrosa, “A class of Steffensen type methods with optimal order of convergence,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7653–7659, 2011.
- Y. Hu and L. Fang, “A seventh-order convergence Newton-type method for solving nonlinear equations,” in 2nd International Conference on Computational Intelligence and Natural Computing, 2010.
- M. A. Noor, W. A. Khan, K. I. Noor, and E. Al-said, “High-order iterative method free from second derivative for solving nonlinear equations,” International Journal of the Physical Science, vol. 6, no. 8, pp. 1887–1893, 2011.
- F. Soleymani and S. K. Khattri, “Finding simple roots by seventh and eighthorder derivative-free methods,” International Journal of Mathematical Models and Methods in Applied Sciences, vol. 1, no. 6, pp. 45–52, 2012.
- S. Amat and S. Busquier, “On a Steffensen's type method and its behavior for semismooth equations,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 819–823, 2006.
- A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A modified Newton-Jarratt's composition,” Numerical Algorithms, vol. 55, no. 1, pp. 87–99, 2010.
- A. Cordero and J. R. Torregrosa, “Variants of Newton's method using fifth-order quadrature formulas,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 686–698, 2007.
- S. Amat and S. Busquier, “On a higher order secant method,” Applied Mathematics and Computation, vol. 141, no. 2-3, pp. 321–329, 2003.