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Article

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Accepted version

Publication date

2016-11-01

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cc-by-nc-nd (c) Elsevier B.V., 2016
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/108550

Newton's method for symmetric quartic polynomials

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https://doi.org/10.1016/j.amc.2016.06.021

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.

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Sistemes dinàmics diferenciables

Subject (English)

Differentiable dynamical systems

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CAMPOS, Beatriz, et al. Newton's method for symmetric quartic polynomials. Applied Mathematics and Computation. 2016. Vol. 290, num. 326-335. ISSN 0096-3003. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/108550

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