# Rigorous numerics for nonlinear operators with tridiagonal dominant linear parts

DC FieldValueLanguage
dc.contributor.authorBreden, Maxime-
dc.contributor.authorDesvillettes, Laurent-
dc.contributor.authorLessard, Jean-Philippe-
dc.date.accessioned2016-05-16T15:26:54Z-
dc.date.available2016-05-16T15:26:54Z-
dc.date.issued2015-04-01-
dc.identifier.issn1078-0947fr_CA
dc.identifier.urihttp://hdl.handle.net/20.500.11794/1301-
dc.description.abstractWe present a method designed for computing solutions of infinite dimensional nonlinear operators f(x) = 0 with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation x = T(x) = x - Af(x), where A is an approximate inverse of the derivative Df(¯x) at an approximate solution ¯x. We present rigorous computer-assisted calculations showing that T is a contraction near ¯x, thus yielding the existence of a solution. Since Df(¯x) does not have an asymptotically diagonal dominant structure, the computation of A is not straightforward. This paper provides ideas for computing A, and proposes a new rigorous method for proving existence of solutions of nonlinear operators with tridiagonal dominant linear part.fr_CA
dc.languageengfr_CA
dc.publisherDept. of Mathematics, Southwest Missouri State Universityfr_CA
dc.subjectTridiagonal operatorfr_CA
dc.subjectContraction mappingfr_CA
dc.subjectRigorous numericsfr_CA
dc.subjectFourier seriesfr_CA
dc.titleRigorous numerics for nonlinear operators with tridiagonal dominant linear partsfr_CA
dc.typeCOAR1_1::Texte::Périodique::Revue::Contribution à un journal::Article::Article de recherche-
dcterms.bibliographicCitationDiscrete and Continuous Dynamical Systems, Vol. 35 (10), 4765–4789 (2015)fr_CA
dc.audienceProfesseurs (Enseignement supérieur)fr_CA
dc.audienceÉtudiantsfr_CA
dc.audienceDoctorantsfr_CA
dc.audienceMathématiciensfr_CA
dc.identifier.doi10.3934/dcds.2015.35.4765fr_CA
dc.identifier.arxiv1503.06315fr_CA
dc.subject.rvmAnalyse numériquefr_CA
dc.subject.rvmSéries de Fourierfr_CA
dc.subject.rvmOpérateurs non linéairesfr_CA
rioxxterms.versionAccepted Manuscriptfr_CA
rioxxterms.version_of_recordhttps://doi.org/10.3934/dcds.2015.35.4765fr_CA
rioxxterms.project.funder_nameNatural Sciences and Engineering Research Council of Canadafr_CA
bul.rights.periodeEmbargo12 moisfr_CA
Collection:Articles publiés dans des revues avec comité de lecture

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