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Damped Traub’s method: Convergence and stability

Author

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  • Cordero, Alicia
  • Ferrero, Alfredo
  • Torregrosa, Juan R.

Abstract

In this paper, a parametric family including Newton’s and Traub’s iterative schemes is presented. Its local convergence and dynamical behavior on quadratic polynomials are studied. The analysis of fixed and critical points and the associated parameter plane show the dynamical richness of the family and allow us to find members of it with good numerical properties, as well as other ones with very unstable behavior.

Suggested Citation

  • Cordero, Alicia & Ferrero, Alfredo & Torregrosa, Juan R., 2016. "Damped Traub’s method: Convergence and stability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 57-68.
    • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:57-68
    DOI: 10.1016/j.matcom.2015.08.012
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    Cited by:

    1. Vázquez-Lozano, J. Enrique & Cordero, Alicia & Torregrosa, Juan R., 2018. "Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 82-99.

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