Dynamics of a family of Chebyshev-Halley type methods. (English) Zbl 1288.65065
Summary: 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.
MSC:
| 65H05 | Numerical computation of solutions to single equations |
Keywords:
nonlinear equations; iterative methods; dynamical behavior; quadratic polynomials; Fatou and Julia sets; Chebyshev-Halley method; non-convergence regionsReferences:
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