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Study of a Biparametric Family of Iterative Methods

Author

Listed:
  • B. Campos
  • A. Cordero
  • Á. A. Magreñán
  • J. R. Torregrosa
  • P. Vindel

Abstract

The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c‐iterative methods and the well‐known Chebyshev‐Halley family. We find the analytical expressions for the fixed and critical points by solving 6‐degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c) with clear stable and unstable behaviors.

Suggested Citation

  • B. Campos & A. Cordero & Á. A. Magreñán & J. R. Torregrosa & P. Vindel, 2014. "Study of a Biparametric Family of Iterative Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:141643
    DOI: 10.1155/2014/141643
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    References listed on IDEAS

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    1. Alicia Cordero & Juan R. Torregrosa & Pura Vindel, 2013. "Bulbs of Period Two in the Family of Chebyshev-Halley Iterative Methods on Quadratic Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, May.
    2. Alicia Cordero & Juan R. Torregrosa & Pura Vindel, 2013. "Bulbs of Period Two in the Family of Chebyshev‐Halley Iterative Methods on Quadratic Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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