General convergence of the methods from Chebyshev-Halley family

Authors

  • Raluca Anamaria Pomian Secondary School Nicolae Bălcescu, Baia Mare, Romania

DOI:

https://doi.org/10.33993/jnaat371-879

Keywords:

Chebyshev-Halley family of iterative methods, basin of attraction, fixed point, periodic point, attracting periodic point
Abstract views: 215

Abstract

In this paper we study the Chebyshev-Halley family (which contains, as particular cases, the Chebyshev method, Halley method, super-Halley method and the C-method). For Chebyshev and super-Halley methods we give a global theorem of convergence. In the end of the paper we study the basins of attraction of the roots of a polynomial with real coefficients. They are obtained when we apply to that polynomial the methods from the Chebyshev-Halley family methods.

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References

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Published

2008-02-01

How to Cite

Pomian, R. A. (2008). General convergence of the methods from Chebyshev-Halley family. Rev. Anal. Numér. Théor. Approx., 37(1), 87–97. https://doi.org/10.33993/jnaat371-879

Issue

Vol. 37 No. 1 (2008)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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