Holomorphic motions in the parameter space for the relaxed Newton's method.
Kriete, Hartje
Kodai Math. J., Tome 25 (2002) no. 2, p. 89-107 / Harvested from Project Euclid
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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.
Publié le : 2002-06-14
Classification:  
@article{1071674434,
     author = {Kriete, Hartje},
     title = {Holomorphic motions in the parameter space for the relaxed Newton's method.},
     journal = {Kodai Math. J.},
     volume = {25},
     number = {2},
     year = {2002},
     pages = { 89-107},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1071674434}
}

Kriete, Hartje. Holomorphic motions in the parameter space for the relaxed Newton's method.. Kodai Math. J., Tome 25 (2002) no. 2, pp.  89-107. http://gdmltest.u-ga.fr/item/1071674434/