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Convergence of gradient-based algorithms for the Hartree-Fock equations

dc.contributor.authorLevitt, Antoine
HAL ID: 8828
dc.date.accessioned2011-09-26T11:55:21Z
dc.date.available2011-09-26T11:55:21Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7010
dc.language.isoenen
dc.subjectŁojasiewicz inequalityen
dc.subjectHartree-Fock equationsen
dc.subjectoptimization on manifoldsen
dc.subject.ddc520en
dc.titleConvergence of gradient-based algorithms for the Hartree-Fock equationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which many algorithms exist. Attempts to justify these algorithms mathematically have been made, notably by Cancès and Le Bris in 2000, but no algorithm has yet been proved to convergence satisfactorily. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient inequality for analytic functionals due to Lojasiewicz. Then, expanding upon the analysis of Cancès and Le Bris, we prove convergence results for the Roothaan and Level-Shifting algorithms. In each case, our method of proof provides estimates on the convergence rate. We compare these with numerical results for the algorithms studied.en
dc.relation.isversionofjnlnameModélisation mathématique et analyse numérique
dc.relation.isversionofjnlvol46
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages1321-1336
dc.relation.isversionofdoihttp://dx.doi.org/10.1051/m2an/2012008
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00626060/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherEDP Sciences
dc.subject.ddclabelSciences connexes (physique, astrophysique)en


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