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 $p$, $p'$...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2016 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/108550 |
| Acesso em linha: | https://hdl.handle.net/2445/108550 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Sistemes dinàmics diferenciables Differentiable dynamical systems |
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oai:diposit.ub.edu:2445/108550 |
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Newton's method for symmetric quartic polynomials Campos, Beatriz Garijo Real, Antonio Jarque i Ribera, Xavier Vindel, Pura Sistemes dinàmics diferenciables Differentiable dynamical systems 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. Elsevier B.V. https://hdl.handle.net/2445/108550 |
| 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 |
| 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 |
| topic |
Sistemes dinàmics diferenciables Differentiable dynamical systems |
| topic_facet |
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 |
| format |
article |
| status_str |
acceptedVersion |
| url |
https://hdl.handle.net/2445/108550 |
| eu_rights_str_mv |
openAccess |
| publisher |
Elsevier B.V. |
| institution |
Universidad de Barcelona |
| collection |
Dipòsit Digital de la UB |
| reponame_str |
Dipòsit Digital de la UB |
| instname_str |
Universidad de Barcelona |
| _version_ |
1878436986674479104 |
| publishDateSort |
2016 |
| author_browse |
Campos, Beatriz Garijo Real, Antonio Jarque i Ribera, Xavier Vindel, Pura |
| publisherStr |
Elsevier B.V. |
| score |
6.9303427 |