Convergence regions for the Chebyshev--Halley family

Abstract

In this paper, we study the dynamical behaviour of the Chebyshev--Halley family applied on a family of degree n polynomials. For n=2 we bound the set of parameters for which the iterative methods have convergence regions which do not correspond to the basins of attraction of the roots. We also study the dynamics of indifferent fixed points on the boundary of the regions of parameters with bad behaviour. Finally, we provide a numerical study on the boundedness of the regions of parameters with bad behaviour for the family of degree n polynomials.