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Basins of attraction for several third order methods to find multiple roots of nonlinear equations

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  • Chun, Changbum
  • Neta, Beny

Abstract

There are several third order methods for solving a nonlinear algebraic equation having roots of a given multiplicity m. Here we compare a recent family of methods of order three to Euler–Cauchy’s method which is found to be the best in the previous work. There are fewer fourth order methods for multiple roots but we will not include them here.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:129-137
    DOI: 10.1016/j.amc.2015.06.068
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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. 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.
    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. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 387-400.
    2. Petković, I. & Herceg, Ð., 2017. "Symbolic computation and computer graphics as tools for developing and studying new root-finding methods," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 95-113.
    3. 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.

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