Newton's method for symmetric quartic polynomials

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 $p$, $p'$...

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Detalles Bibliográficos
Autores: Campos, Beatriz, Garijo Real, Antonio, Jarque i Ribera, Xavier, Vindel, Pura
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/108550
Acceso en línea:https://hdl.handle.net/2445/108550
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics diferenciables
Differentiable dynamical systems
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spelling Newton's method for symmetric quartic polynomialsCampos, BeatrizGarijo Real, AntonioJarque i Ribera, XavierVindel, PuraSistemes dinàmics diferenciablesDifferentiable dynamical systemsWe 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.Elsevier B.V.2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/108550Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1016/j.amc.2016.06.021Applied Mathematics and Computation, 2016, vol. 290, p. 326-335https://doi.org/10.1016/j.amc.2016.06.021cc-by-nc-nd (c) Elsevier B.V., 2016http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1085502026-05-27T06:46:51Z
dc.title.none.fl_str_mv Newton's method for symmetric quartic polynomials
title Newton's method for symmetric quartic polynomials
spellingShingle Newton's method for symmetric quartic polynomials
Campos, Beatriz
Sistemes dinàmics diferenciables
Differentiable dynamical systems
title_short Newton's method for symmetric quartic polynomials
title_full Newton's method for symmetric quartic polynomials
title_fullStr Newton's method for symmetric quartic polynomials
title_full_unstemmed Newton's method for symmetric quartic polynomials
title_sort Newton's method for symmetric quartic polynomials
dc.creator.none.fl_str_mv Campos, Beatriz
Garijo Real, Antonio
Jarque i Ribera, Xavier
Vindel, Pura
author Campos, Beatriz
author_facet Campos, Beatriz
Garijo Real, Antonio
Jarque i Ribera, Xavier
Vindel, Pura
author_role author
author2 Garijo Real, Antonio
Jarque i Ribera, Xavier
Vindel, Pura
author2_role author
author
author
dc.subject.none.fl_str_mv Sistemes dinàmics diferenciables
Differentiable dynamical systems
topic Sistemes dinàmics diferenciables
Differentiable dynamical systems
description 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.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/108550
url https://hdl.handle.net/2445/108550
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.amc.2016.06.021
Applied Mathematics and Computation, 2016, vol. 290, p. 326-335
https://doi.org/10.1016/j.amc.2016.06.021
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier B.V., 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier B.V., 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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