Dynamics of the Secant map near infinity

IWe investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on (Formula presented.). We extend the Secant map to the real projective plane (Formula presented.). The line at infinity (Formula presented.) is in...

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Detalles Bibliográficos
Autores: Garijo, A., Jarque, X.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/531792
Acceso en línea:http://hdl.handle.net/2072/531792
Access Level:acceso abierto
Palabra clave:Iteration
Root finding algorithms
Secant method
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spelling Dynamics of the Secant map near infinityGarijo, A.Jarque, X.IterationRoot finding algorithmsSecant methodIWe investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on (Formula presented.). We extend the Secant map to the real projective plane (Formula presented.). The line at infinity (Formula presented.) is invariant, and there is one (if k is odd) or two (if k is even) fixed points at (Formula presented.). We show that these are of saddle type, and this allows us to better understand the dynamics of the Secant map near infinity. © 2022 Informa UK Limited, trading as Taylor & Francis Group.PID2020-118281GB-C32, PID2020-118281GB-C33; Agència de Gestió d'Ajuts Universitaris i de Recerca, AGAUR: 2017SGR1374. This work also acknowledges the CERCA Programme of the Generalitat de Catalunya for institutional support. This work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M).Journal of Difference Equations and Applications2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion13 p.application/pdfhttp://hdl.handle.net/2072/531792RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésTaylor and Francis Ltd.L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5317922026-05-29T05:05:01Z
dc.title.none.fl_str_mv Dynamics of the Secant map near infinity
title Dynamics of the Secant map near infinity
spellingShingle Dynamics of the Secant map near infinity
Garijo, A.
Iteration
Root finding algorithms
Secant method
title_short Dynamics of the Secant map near infinity
title_full Dynamics of the Secant map near infinity
title_fullStr Dynamics of the Secant map near infinity
title_full_unstemmed Dynamics of the Secant map near infinity
title_sort Dynamics of the Secant map near infinity
dc.creator.none.fl_str_mv Garijo, A.
Jarque, X.
author Garijo, A.
author_facet Garijo, A.
Jarque, X.
author_role author
author2 Jarque, X.
author2_role author
dc.subject.none.fl_str_mv Iteration
Root finding algorithms
Secant method
topic Iteration
Root finding algorithms
Secant method
description IWe investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on (Formula presented.). We extend the Secant map to the real projective plane (Formula presented.). The line at infinity (Formula presented.) is invariant, and there is one (if k is odd) or two (if k is even) fixed points at (Formula presented.). We show that these are of saddle type, and this allows us to better understand the dynamics of the Secant map near infinity. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
publishDate 2022
dc.date.none.fl_str_mv 2022
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 http://hdl.handle.net/2072/531792
url http://hdl.handle.net/2072/531792
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Taylor and Francis Ltd.
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 13 p.
application/pdf
dc.publisher.none.fl_str_mv Journal of Difference Equations and Applications
publisher.none.fl_str_mv Journal of Difference Equations and Applications
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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