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One-Point Optimal Family of Multiple Root Solvers of Second-Order

Author

Listed:
  • Deepak Kumar

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India)

  • Janak Raj Sharma

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

Abstract

This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure of weight functions. The convergence behavior is discussed by showing some essential conditions of the weight function. The well-known modified Newton method is a member of the proposed family for particular choices of the weight function. The dynamical nature of different members is presented by using a technique called the “basin of attraction”. Several practical problems are given to compare different methods of the presented family.

Suggested Citation

  • Deepak Kumar & Janak Raj Sharma & Clemente Cesarano, 2019. "One-Point Optimal Family of Multiple Root Solvers of Second-Order," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:655-:d:250370
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    References listed on IDEAS

    as
    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. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2016. "A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 120-140.
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    Cited by:

    1. Deepak Kumar & Janak Raj Sharma & Ioannis K. Argyros, 2020. "Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots," Mathematics, MDPI, vol. 8(5), pages 1-14, May.

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