Date
2012
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http://hal.archives-ouvertes.fr/hal-00626060/fr/
Indexation documentaire
Sciences connexes (physique, astrophysique)
Subject
Łojasiewicz inequality; Hartree-Fock equations; optimization on manifolds
Nom de la revue
Modélisation mathématique et analyse numérique
Volume
46
Numéro
6
Date de publication
2012
Pages article
1321-1336
Nom de l'éditeur
EDP Sciences
Type
Article accepté pour publication ou publié
Résumé en anglais
The 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.