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Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane

Author

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  • Magreñán, Á. Alberto
  • Cordero, Alicia
  • Gutiérrez, José M.
  • Torregrosa, Juan R.

Abstract

The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used to obtain the same kind of information as from the parameter space, and even more, in complex dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:105:y:2014:i:c:p:49-61
    DOI: 10.1016/j.matcom.2014.04.006
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. F. I. Chicharro & A. Cordero & J. R. Torregrosa & M. P. Vassileva, 2017. "King-Type Derivative-Free Iterative Families: Real and Memory Dynamics," Complexity, Hindawi, vol. 2017, pages 1-15, October.
    4. Geum, Young Hee & Kim, Young Ik & Magreñán, Á. Alberto, 2016. "A biparametric extension of King’s fourth-order methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 254-275.
    5. 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.
    6. 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.
    7. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2020. "Impact on Stability by the Use of Memory in Traub-Type Schemes," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    8. Lee, Min-Young & Ik Kim, Young & Alberto Magreñán, Á., 2017. "On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-to function ratio," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 564-590.
    9. Chun, Changbum & Neta, Beny, 2016. "An analysis of a Khattri’s 4th order family of methods," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 198-207.

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