Abstract
It is a well known fact, that for certain polynomials $f$ the relaxed Newton's method $N_{f,h}(z) = z - h\frac{f(z)}{f'(z)}$ associated with $f$ has some extraneous attracting cycles. In the case of cubic polynomials the set of these bad conditioned polynomials has been intensively studied and described by means of quasi--holomorphic surgery and holomorphic motions, cf.~\cite{haeseler:1988}. In the present paper we will generalize this description to polynomials of higher degree.
Citation
Hartje Kriete. "Holomorphic motions in the parameter space for the relaxed Newton's method.." Kodai Math. J. 25 (2) 89 - 107, June 2002. https://doi.org/10.2996/kmj/1071674434
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