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

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00626060/fr/
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Łojasiewicz inequality; Hartree-Fock equations; optimization on manifolds
Journal issue
Modélisation mathématique et analyse numérique
Volume
46
Number
6
Publication date
2012
Article pages
1321-1336
Publisher
EDP Sciences
DOI
http://dx.doi.org/10.1051/m2an/2012008
URI
https://basepub.dauphine.fr/handle/123456789/7010
Collections
  • CEREMADE : Publications
Metadata
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Author
Levitt, Antoine
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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