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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 979245, 13 pages
On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations
1Department of Applied Mathematical Sciences, School of Innovative Technologies and Engineering,
University of Technology, Mauritius, La Tour Koenig, Pointe aux Sables, Mauritius
2Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire LS17 5JS, UK
Received 23 March 2012; Accepted 14 May 2012
Academic Editor: Songxiao Li
Copyright © 2012 Diyashvir Kreetee Rajiv Babajee and Rajinder Thukral. 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. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, New Jersey, NJ, USA, 1964.
- 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.
- J. M. McNamee, Numerical Methods for Roots of Polynomial: Part 1, Elsevier, Amsterdam, The Netherlands, 2007.
- M. S. Petković and L. D. Petković, “Families of optimal multipoint methods for solving nonlinear equations: a survey,” Applicable Analysis and Discrete Mathematics, vol. 4, no. 1, pp. 1–22, 2010.
- R. Wait, The Numerical Solution of Algebraic Equations, John Wiley & Sons, New York, NY, USA, 1979.
- A. M. Ostrowski, Solutions of Equations and System of Equations, Academic Press, New York, NY, USA, 1960.
- H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, vol. 21, no. 4, pp. 643–651, 1974.
- S. Weerakoon and T. G. I. Fernando, “A variant of newton's method with accelerated third-order convergence,” Applied Mathematics Letters, vol. 13, no. 8, pp. 87–93, 2000.
- R. F. King, “A family of fourth order methods for nonlinear equations,” SIAM Journal on Numerical Analysis, vol. 10, pp. 876–879, 1973.
- W. Bi, H. Ren, and Q. Wu, “Three-step iterative methods with eighth-order convergence for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 105–112, 2009.
- W. Bi, Q. Wu, and H. Ren, “A new family of eighth-order iterative methods for solving nonlinear equations,” Applied Mathematics and Computation, vol. 214, no. 1, pp. 236–245, 2009.
- B. Neta, “On a family of multipoint methods for nonlinear equations,” International Journal of Computer Mathematics, vol. 9, no. 4, pp. 353–361, 1981.
- R. Thukral and M. S. Petković, “A family of three-point methods of optimal order for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 233, no. 9, pp. 2278–2284, 2010.
- 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.
- 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 and Mathematics with Applications, vol. 61, no. 11, pp. 3278–3287, 2011.
- D. K. R. Babajee and M. Z. Dauhoo, “An analysis of the properties of the variants of newton's method with third order convergence,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 659–684, 2006.
- M. Drexler, Newton's Method as a Global Solver for Non-Linear Problems [Ph.D. thesis], University of Oxford, Oxford, UK, 1997.