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Study of a Biparametric Family of Iterative Methods

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  • 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 -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 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, Hindawi, vol. 2014, pages 1-12, December.
    • Handle: RePEc:hin:jnlaaa:141643
    DOI: 10.1155/2014/141643
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