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A family of optimal quartic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction

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  • Geum, Young Hee
  • Kim, Young Ik
  • Neta, Beny

Abstract

Multiple-zero finders with optimal quartic convergence for nonlinear equations are proposed in this paper with a weight function of the principal kth root of a derivative-to-derivative ratio. The optimality of the proposed multiple-zero finders is checked for their consistency based on Kung–Traub’s conjecture established in 1974. Through various test equations, relevant numerical experiments strongly support the claimed theory in this paper. Also investigated are extraneous fixed points of the iterative maps associated with the proposed methods. Their dynamics is explored along with illustrated basins of attraction for various polynomials.

Suggested Citation

  • Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2017. "A family of optimal quartic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 1-21.
    • Handle: RePEc:eee:matcom:v:136:y:2017:i:c:p:1-21
    DOI: 10.1016/j.matcom.2016.10.008
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    References listed on IDEAS

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    1. Neta, Beny & Chun, Changbum, 2014. "Basins of attraction for several optimal fourth order methods for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 103(C), pages 39-59.
    2. Magreñán, Á. Alberto & Cordero, Alicia & Gutiérrez, José M. & Torregrosa, Juan R., 2014. "Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 49-61.
    3. Chun, Changbum & Neta, Beny, 2015. "Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 74-91.
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    Cited by:

    1. Francisco I. Chicharro & Rafael A. Contreras & Neus Garrido, 2020. "A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.

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