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A Two‐Parameter Family of Fourth‐Order Iterative Methods with Optimal Convergence for Multiple Zeros

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  • Young Ik Kim
  • Young Hee Geum

Abstract

We develop a family of fourth‐order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung‐Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods.

Suggested Citation

  • Young Ik Kim & Young Hee Geum, 2013. "A Two‐Parameter Family of Fourth‐Order Iterative Methods with Optimal Convergence for Multiple Zeros," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:369067
    DOI: 10.1155/2013/369067
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    References listed on IDEAS

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    1. F. Soleymani & S. Shateyi & H. Salmani, 2012. "Computing Simple Roots by an Optimal Sixteenth‐Order Class," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. F. Soleymani & S. Shateyi & H. Salmani, 2012. "Computing Simple Roots by an Optimal Sixteenth-Order Class," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, November.
    3. F. Soleymani & D. K. R. Babajee & S. Shateyi & S. S. Motsa, 2012. "Construction of Optimal Derivative‐Free Techniques without Memory," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. F. Soleymani & D. K. R. Babajee & S. Shateyi & S. S. Motsa, 2012. "Construction of Optimal Derivative-Free Techniques without Memory," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, November.
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    Cited by:

    1. Young Ik Kim & Young Hee Geum, 2016. "A Triparametric Family of Optimal Fourth‐Order Multiple‐Root Finders and Their Dynamics," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    2. Mohammed Barrada & Mariya Ouaissa & Yassine Rhazali & Mariyam Ouaissa, 2020. "A New Class of Halley’s Method with Third‐Order Convergence for Solving Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    3. Young Ik Kim & Young Hee Geum, 2014. "A New Biparametric Family of Two‐Point Optimal Fourth‐Order Multiple‐Root Finders," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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