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The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable

2021Journal article Restricted access
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dc.contributor.authorGraça, Daniel
dc.contributor.authorZhong, Ning
dc.date.accessioned2021-11-30T17:50:19Z
dc.date.available2021-11-30T17:50:19Z
dc.date.issued2021
dc.description.abstractIn this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations with arbitrary accuracy. By arbitrary accuracy it is meant that any accuracy required by the input can be achieved. The algorithm can be further extended to a root-finding algorithm that computes the exact number of zeros as well the location of each zero of a continuously differentiable function $f$ defined on the closed unit ball of $\mathbb{R}^{d}$, provided that the Jacobian of $f$ is invertible at each zero of $f$; moreover, the computation is uniform in $f$.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.tcs.2021.09.028pt_PT
dc.identifier.eissn1879-2294
dc.identifier.issn0304-3975
dc.identifier.urihttp://hdl.handle.net/10400.1/17359
dc.language.isoengpt_PT
dc.peerreviewednopt_PT
dc.publisherElsevierpt_PT
dc.relationInstituto de Telecomunicações
dc.relationComputing with Infinite Data
dc.relation.hasversionhttps://arxiv.org/pdf/2002.08199.pdf
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectComputabilitypt_PT
dc.subjectComputing the number of zeros of a functionpt_PT
dc.subjectGlobal root-finding algorithmpt_PT
dc.subjectHyperbolic equilibriapt_PT
dc.titleThe set of hyperbolic equilibria and of invertible zeros on the unit ball is computablept_PT
dc.title.alternativeO conjunto de equilíbrio hiperbólico e de zeros invertíveis na bola unitária é computávelpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleInstituto de Telecomunicações
oaire.awardTitleComputing with Infinite Data
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F50008%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/EC/H2020/731143/EU
oaire.citation.endPage54pt_PT
oaire.citation.startPage48pt_PT
oaire.citation.titleTheoretical Computer Sciencept_PT
oaire.citation.volume895pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStreamH2020
person.familyNameGraça
person.givenNameDaniel
person.identifier.ciencia-id2D11-56DE-3F11
person.identifier.orcid0000-0002-0330-833X
person.identifier.ridD-2335-2011
person.identifier.scopus-author-id8882791800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100008530
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameEuropean Commission
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
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