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A NOTE ON THE PAPER ENTITLED SIXTEENTH-ORDER METHOD FOR NONLINEAR EQUATIONS

  • Kim, Young Ik (Department of Applied Mathematics Dankook University)
  • Published : 2012.05.15

Abstract

The purpose of this paper is to provide some corrections regarding algebraic flaws encountered in the paper entitled "Sixteenth-order method for nonlinear equations" which was published in January of 2010 by Li et al.[9]. Further detailed comments on their error equation are stated together with convergence analysis as well as high-precision numerical experiments.

Keywords

References

  1. C. Chun, Y. Ham, Some sixth-order variants of Ostrowski root-finding methods, Applied Mathematics and Computation 193 (2007), 389-394. https://doi.org/10.1016/j.amc.2007.03.074
  2. Y. H. Geum, Y. I. Kim, A multi-parameter family of three-step eighth-order it- erative methods locating a simple root, Applied Mathematics and Computation 215 (2010), 3375-3382. https://doi.org/10.1016/j.amc.2009.10.030
  3. P. Jarratt, Some fourth-order multipoint iterative methods for solving equations, Math. Comput. 20 (1966), no. 95, 434-437. https://doi.org/10.1090/S0025-5718-66-99924-8
  4. R. King, A family of fourth-order methods for nonlinear equations, SIAM J. Numer. Anal. 10 (1973), no. 5, 876-879. https://doi.org/10.1137/0710072
  5. H. T. Kung, J. F. Traub, optimal order of one-point and multipoint iteration, Journal of the Association for Computing Machinery 21 (1974), 643-651. https://doi.org/10.1145/321850.321860
  6. H. Ren, Q. Wu, W. Bi, New variants of Jarratts method with sixth-order convergence, Numer. Algor., (2009).
  7. J. Sharma, R. Guha, A family of modified Ostrowski's methods with accelerated sixth order convergence, Applied Mathematics and Computation 190 (2007), 111-115. https://doi.org/10.1016/j.amc.2007.01.009
  8. J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, 1982.
  9. X. Li, C. Mu, J. Ma, C. Wang, Sixteenth-order method for nonlinear equations, Applied Mathematics and Computation 215 (2010), 3754-3758. https://doi.org/10.1016/j.amc.2009.11.016
  10. S. Wolfram, The Mathematica Book, 5th ed., Wolfram Media, 2003.