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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/159358
Convergence regions for the Chebyshev-Halley family
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In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree $n$ polynomials $z^{n}+c$. We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having $z=\infty $ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of $n$ grows. We also demonstrate that, although the convergence order of the Chebyshev-Halley family is 3, there is a member of order 4 for each value of $n$. In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots.
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CAMPOS, Beatriz, CANELA SÁNCHEZ, Jordi and VINDEL, Pura. Convergence regions for the Chebyshev-Halley family. Communications In Nonlinear Science And Numerical Simulation. 2018. Vol. 56, num. 508-525. ISSN 1007-5704. [consulted: 25 of May of 2026]. Available at: https://hdl.handle.net/2445/159358