Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

A SEXTIC-ORDER VARIANT OF DOUBLE-NEWTON METHODS WITH A SIMPLE BIVARIATE WEIGHTING FUNCTION

  • Kim, Young Ik (Department of Applied Mathematics Dankook University)
  • Received : 2014.07.25
  • Accepted : 2014.08.05
  • Published : 2014.08.15
Download PDF
⟨ Previous Next ⟩

Abstract

Via extension of the classical double-Newton method, we propose high-order family of two-point methods in this paper. Theoretical and computational properties of the proposed methods are fully investigated along with a main theorem describing methodology and convergence analysis. Typical numerical examples are thoroughly treated to verify the underlying theory.

Keywords

References

  1. L. V. Ahlfors, Complex Analysis, McGraw-Hill Book, Inc., 1979.
  2. W. Bi, Q. Wu, and H. Ren, A new family of eighth-order iterative methods for solving nonlinear equations, Appl. Math. Comput. 214 (2009), no. 4, 236-245. https://doi.org/10.1016/j.amc.2009.03.077
  3. C. Chun, Some improvements of Jarratts method with sextic-order convergence, Appl. Math. Comput. 190 (2007), 1432-1437. https://doi.org/10.1016/j.amc.2007.02.023
  4. Y. H. Geum and Y. I. Kim, A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index, Appl. Math. Lett. 24 (2011), 1336-1342. https://doi.org/10.1016/j.aml.2011.03.004
  5. P. Jarratt, Multipoint iterative methods for solving certain equations, Comput. J. 8 (1966), no. 4, 398-400. https://doi.org/10.1093/comjnl/8.4.398
  6. H. T. Kung and J. F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Mach. 21 (1974), 643-651. https://doi.org/10.1145/321850.321860
  7. S. K. Parhi and D. K. Gupta, A sixth order method for nonlinear equations, Appl. Math. Comput. 203 (2008), 50-55. https://doi.org/10.1016/j.amc.2008.03.037
  8. Y. Peng, H. Feng, Q. Li, and X. Zhang, A fourth-order derivative-free algorithm for nonlinear equations, J. Comput. Appl. Math. 235 (2011), 2551-2559. https://doi.org/10.1016/j.cam.2010.11.007
  9. J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, 1982.
  10. S. Wolfram, The Mathematica Book, 5th ed., Wolfram Media, 2003.