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On the dynamics of a family of third-order iterative functions

  • Sergio Amat, Sonia Busquier and Sergio Plaza

Abstract

We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.

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References

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On the dynamics of a family of third-order iterative functions

  • Sergio Amat, Sonia Busquier and Sergio Plaza

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