Topological properties of the immediate basins of attraction for the secant method

We study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. We denote by...

Descripción completa

Detalles Bibliográficos
Autores: Gardini, Laura|||0000-0002-3386-6543, Garijo, Antoni|||0000-0002-1503-7514, Jarque i Ribera, Xavier|||0000-0002-6576-9780
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257106
Acceso en línea:https://ddd.uab.cat/record/257106
https://dx.doi.org/urn:doi:10.1007/s00009-021-01845-y
Access Level:acceso abierto
Palabra clave:Root finding algorithms
Rational iteration
Secant method
Periodic orbits
id ES_3fedd0128cef3c21e7c4bbbef7a701b9
oai_identifier_str oai:ddd.uab.cat:257106
network_acronym_str ES
network_name_str España
repository_id_str
spelling Topological properties of the immediate basins of attraction for the secant methodGardini, Laura|||0000-0002-3386-6543Garijo, Antoni|||0000-0002-1503-7514Jarque i Ribera, Xavier|||0000-0002-6576-9780Root finding algorithmsRational iterationSecant methodPeriodic orbitsWe study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. We denote by A(α) its immediate basin of attraction, that is, the connected component of A(α) which contains (α, α). We focus on some topological properties of A(α), when α is an internal real root of p. More precisely, we show the existence of a 4-cycle in ∂A(α) and we give conditions on p to guarantee the simple connectivity of A(α). 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/257106https://dx.doi.org/urn:doi:10.1007/s00009-021-01845-yreponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM-2017-86795-C3-2-PAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM-2017-86795-C3-3-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1374open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2571062026-06-06T12:50:31Z
dc.title.none.fl_str_mv Topological properties of the immediate basins of attraction for the secant method
title Topological properties of the immediate basins of attraction for the secant method
spellingShingle Topological properties of the immediate basins of attraction for the secant method
Gardini, Laura|||0000-0002-3386-6543
Root finding algorithms
Rational iteration
Secant method
Periodic orbits
title_short Topological properties of the immediate basins of attraction for the secant method
title_full Topological properties of the immediate basins of attraction for the secant method
title_fullStr Topological properties of the immediate basins of attraction for the secant method
title_full_unstemmed Topological properties of the immediate basins of attraction for the secant method
title_sort Topological properties of the immediate basins of attraction for the secant method
dc.creator.none.fl_str_mv Gardini, Laura|||0000-0002-3386-6543
Garijo, Antoni|||0000-0002-1503-7514
Jarque i Ribera, Xavier|||0000-0002-6576-9780
author Gardini, Laura|||0000-0002-3386-6543
author_facet Gardini, Laura|||0000-0002-3386-6543
Garijo, Antoni|||0000-0002-1503-7514
Jarque i Ribera, Xavier|||0000-0002-6576-9780
author_role author
author2 Garijo, Antoni|||0000-0002-1503-7514
Jarque i Ribera, Xavier|||0000-0002-6576-9780
author2_role author
author
dc.subject.none.fl_str_mv Root finding algorithms
Rational iteration
Secant method
Periodic orbits
topic Root finding algorithms
Rational iteration
Secant method
Periodic orbits
description We study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. We denote by A(α) its immediate basin of attraction, that is, the connected component of A(α) which contains (α, α). We focus on some topological properties of A(α), when α is an internal real root of p. More precisely, we show the existence of a 4-cycle in ∂A(α) and we give conditions on p to guarantee the simple connectivity of A(α).
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/257106
https://dx.doi.org/urn:doi:10.1007/s00009-021-01845-y
url https://ddd.uab.cat/record/257106
https://dx.doi.org/urn:doi:10.1007/s00009-021-01845-y
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM-2017-86795-C3-2-P
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM-2017-86795-C3-3-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1374
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869406700940820480
score 15,301603

Similares en LA Referencia