2024-03-29T11:59:13Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/942762023-03-01T13:25:16Zcom_10234_7037com_10234_9col_10234_8635
00925njm 22002777a 4500
dc
Cordero Barbero, Alicia
author
Torregrosa, Juan R.
author
Vindel, Pura
author
2013-04-15
In this paper, the dynamics of the Chebyshev–Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This set has interesting similarities with the Mandelbrot set. The parameter space has allowed us to find different elements of the family which have bad convergence properties, since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method
CORDERO, A.; TORREGROSA, J. R..; VINDEL, P. Dynamics of a family of Chebyshev-Halley type methods. Applied Mathematics and Computation, Volume 219, Issue 16 (15 April 2013), Pages 8568–8583
http://hdl.handle.net/10234/94276
http://dx.doi.org/10.1016/j.amc.2013.02.042
Nonlinear equations
Iterative methods
Dynamical behavior
Quadratic polynomials
Fatou and Julia sets
Chebyshev–Halley method
Non-convergence regions
Dynamics of a family of Chebyshev-Halley