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Title: Newton's method for symmetric quartic polynomials
Author: Beatriz, Campos
Garijo Real, Antonio
Jarque i Ribera, Xavier
Vindel, Pura
Keywords: Sistemes dinàmics diferenciables
Differentiable dynamical systems
Issue Date: 1-Nov-2016
Publisher: Elsevier B.V.
Abstract: We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials $p_{a,b}(z)=z^4+az^3+bz^2+az+1$, where $a$ and $b$ are real parameters. We divide the parameter plane $(a,b) \in \mathbb R^2$ into twelve open and connected {\it regions} where $p$, $p'$ and $p''$ have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere.
Note: Versió postprint del document publicat a:
It is part of: Applied Mathematics and Computation, 2016, vol. 290, p. 326-335
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ISSN: 0096-3003
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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