Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/159358
Title: | Convergence regions for the Chebyshev-Halley family |
Author: | Campos, Beatriz Canela Sánchez, Jordi Vindel, Pura |
Keywords: | Sistemes de Chebyshev Polinomis Chebyshev systems Polynomials |
Issue Date: | 2018 |
Publisher: | Elsevier B.V. |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2017.08.024 |
It is part of: | Communications In Nonlinear Science And Numerical Simulation, 2018, vol. 56, p. 508-525 |
URI: | http://hdl.handle.net/2445/159358 |
Related resource: | https://doi.org/10.1016/j.cnsns.2017.08.024 |
ISSN: | 1007-5704 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
673448.pdf | 4.81 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License