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Comparison of several families of optimal eighth order methods

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  • Chun, Changbum
  • Neta, Beny

Abstract

Several families of optimal eighth order methods to find simple roots are compared to the best known eighth order method due to Wang and Liu (2010). We have tried to improve their performance by choosing the free parameters of each family using two different criteria.

Suggested Citation

  • Chun, Changbum & Neta, Beny, 2016. "Comparison of several families of optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 762-773.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:762-773
    DOI: 10.1016/j.amc.2015.10.092
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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. Chun, Changbum & Neta, Beny, 2015. "Basins of attraction for several third order methods to find multiple roots of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 129-137.
    3. Chun, Changbum & Neta, Beny, 2015. "An analysis of a family of Maheshwari-based optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 294-307.
    4. Argyros, Ioannis K. & Magreñán, Á. Alberto, 2015. "On the convergence of an optimal fourth-order family of methods and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 336-346.
    5. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "On developing a higher-order family of double-Newton methods with a bivariate weighting function," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 277-290.
    6. Chun, Changbum & Neta, Beny, 2015. "Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 277-292.
    7. 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. Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2017. "Generating function method for constructing new iterations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 414-423.
    2. Min-Young Lee & Young Ik Kim & Beny Neta, 2019. "A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points," Mathematics, MDPI, vol. 7(6), pages 1-26, June.
    3. Young Hee Geum & Young Ik Kim & Beny Neta, 2018. "Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics," Mathematics, MDPI, vol. 7(1), pages 1-32, December.

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