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| HAL: hal-00626060, version 2 |
| arXiv: 1109.5473 |
| DOI: 10.1051/m2an/2012008 |
| Detailed view |  Export this paper |
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| ESAIM: Mathematical Modelling and Numerical Analysis 46, 06 (2012) 1321-1336 |
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| Available versions: | v1 (2011-09-26) | v2 (2012-02-01) |
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| Convergence of gradient-based algorithms for the Hartree-Fock equations |
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| Antoine Levitt 1 |
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| (2012-11) |
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| The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in by Cances and Le Bris in 2000, but, to our knowledge, no complete convergence proof has been published. 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 Cances 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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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Mathematics/Mathematical Physics Mathematics/Analysis of PDEs Mathematics/Numerical Analysis |
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| Hartree-Fock equations – Lojasiewicz inequality – optimization on manifolds |
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| hal-00626060, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00626060 | |
| oai:hal.archives-ouvertes.fr:hal-00626060 | |
| From: Antoine Levitt | |
| Submitted on: Wednesday, 1 February 2012 09:37:07 | |
| Updated on: Wednesday, 23 May 2012 13:27:43 | |
