Abstract
We consider the desingularized continuous Newton-method for rational functions of one complex variable. Structural stability aspects are discussed. Special attention is given to rational functions with one (simple) pole. For these functions a full classification — up to topological equivalence — is obtained.
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Jongen, H.T., Jonker, P., Twilt, F. (1980). Some Reflections on the Continuous Newton-Method for Rational Functions. In: Collatz, L., Meinardus, G., Wetterling, W. (eds) Konstruktive Methoden der finiten nichtlinearen Optimierung. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6322-3_8
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DOI: https://doi.org/10.1007/978-3-0348-6322-3_8
Publisher Name: Birkhäuser, Basel
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