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An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations

Author

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  • Young Hee Geum

    (Dankook University)

  • Young Ik Kim

    (Dankook University)

Abstract

This paper investigates an optimal family of derivative-free fast 16th-order multipoint iterative methods for solving nonlinear equations using polynomial weighting functions and a real control parameter. Convergence analyses and computational properties are shown along with a comparison of the classical work done by Kung–Traub in 1974. The underlying theoretical treatment and computational advantage of faster computing time is well supported through a variety of concrete numerical examples.

Suggested Citation

  • Young Hee Geum & Young Ik Kim, 2014. "An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 608-622, February.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0268-x
    DOI: 10.1007/s10957-013-0268-x
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    References listed on IDEAS

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    1. A. Germani & C. Manes & P. Palumbo & M. Sciandrone, 2006. "Higher-Order Method for the Solution of a Nonlinear Scalar Equation," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 347-364, December.
    2. Fazlollah Soleymani & Mahdi Sharifi & Bibi Somayeh Mousavi, 2012. "An Improvement of Ostrowski’s and King’s Techniques with Optimal Convergence Order Eight," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 225-236, April.
    3. Min Chen & Tsu-Shuan Chang, 2011. "On the Higher-Order Method for the Solution of a Nonlinear Scalar Equation," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 647-664, June.
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