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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 687382, 7 pages
A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence
Department of Environmental Health Science, University of Swaziland, P.O. Box 369, Mbabane H100, Swaziland
Received 25 October 2012; Revised 25 December 2012; Accepted 17 February 2013
Academic Editor: Michele Benzi
Copyright © 2013 Ababu Teklemariam Tiruneh 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.
- C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 5th edition, 1994.
- 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.
- J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- M. Grau-Sánchez and J. L. Díaz-Barrero, “A technique to composite a modified Newton's method for solving nonlinear equations,” Annals of the University of Bucharest, vol. 2, no. 1, pp. 53–61, 2011.
- J. R. Sharma and R. K. Guha, “A family of modified Ostrowski methods with accelerated sixth order convergence,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 111–115, 2007.
- C. Chun, “Some improvements of Jarratt's method with sixth-order convergence,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1432–1437, 2007.
- J. Kou and X. Wang, “Sixth-order variants of Chebyshev-Halley methods for solving non-linear equations,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1839–1843, 2007.
- J. Kou, “On Chebyshev-Halley methods with sixth-order convergence for solving non-linear equations,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 126–131, 2007.
- J. Kou and Y. Li, “An improvement of the Jarratt method,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1816–1821, 2007.
- J. Kou, Y. Li, and X. Wang, “Some modifications of Newton's method with fifth-order convergence,” Journal of Computational and Applied Mathematics, vol. 209, no. 2, pp. 146–152, 2007.
- S. K. Parhi and D. K. Gupta, “A sixth order method for nonlinear equations,” Applied Mathematics and Computation, vol. 203, no. 1, pp. 50–55, 2008.
- D. E. Muller, “A method for solving algebraic equations using an automatic computer,” Mathematical Tables and Other Aids to Computation, vol. 10, pp. 208–215, 1956.
- W. R. Mekwi, Iterative methods for roots of polynomials [M.S. thesis], University of Oxford, 2001.
- T. J. Dekker, “Finding a zero by means of successive linear interpolation,” in Constructive Aspects of the Fundamental Theorem of Algebra, B. Dejon and P. Henrici, Eds., Wiley-Interscience, London, UK, 1969.
- R. P. Brent, Algorithms for Minimization without Derivatives, chapter 4, Prentice-Hall, Englewood Cliffs, NJ, USA, 1973.
- A. B. Kasturiarachi, “Leap-frogging Newton's method,” International Journal of Mathematical Education in Science and Technology, vol. 33, no. 4, pp. 521–527, 2002.