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A Graphic Method for Detecting Multiple Roots Based on Self-Maps of the Hopf Fibration and Nullity Tolerances

The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation. In fact, we present a collection of algorithms that avoid the problem of overflows cau...

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Kaydedildi:
Asıl Yazarlar: José Ignacio Extreminana-Aldana, José Manuel Gutiérrez-Jiménez, Luis Javier Hernández-Paricio, María Teresa Rivas-Rodríguéz
Materyal Türü: Artigo
Dil:Inglês
Baskı/Yayın Bilgisi: MDPI AG 2021-08-01
Seri Bilgileri:Mathematics
Konular:
Newton’s method
Hopf fibration
multiple roots
rational functions
homogeneous coordinates
Riemann sphere
Online Erişim:https://www.mdpi.com/2227-7390/9/16/1914
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