The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown that the s∗-compressibility is in accordance with convergence rates obtained from best N-term approximation for solutions of the Hartree-Fock equation. This is a necessary requirement in order to achieve numerical solutions for these equations with optimal complexity using the recently developed adaptive wavelet algorithms of Cohen, Dahmen and DeVore.
Mots-clés : Hartree-Fock equation, matrix compression, bestn-term approximation
@article{M2AN_2012__46_5_1055_0,
author = {Flad, Heinz-J\"urgen and Schneider, Reinhold},
title = {$s^\ast $-compressibility of the discrete {Hartree-Fock} equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1055--1080},
publisher = {EDP-Sciences},
volume = {46},
number = {5},
year = {2012},
doi = {10.1051/m2an/2011077},
zbl = {1272.65091},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011077/}
}
TY - JOUR AU - Flad, Heinz-Jürgen AU - Schneider, Reinhold TI - $s^\ast $-compressibility of the discrete Hartree-Fock equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1055 EP - 1080 VL - 46 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011077/ DO - 10.1051/m2an/2011077 LA - en ID - M2AN_2012__46_5_1055_0 ER -
%0 Journal Article %A Flad, Heinz-Jürgen %A Schneider, Reinhold %T $s^\ast $-compressibility of the discrete Hartree-Fock equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1055-1080 %V 46 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011077/ %R 10.1051/m2an/2011077 %G en %F M2AN_2012__46_5_1055_0
Flad, Heinz-Jürgen; Schneider, Reinhold. $s^\ast $-compressibility of the discrete Hartree-Fock equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1055-1080. doi : 10.1051/m2an/2011077. http://www.numdam.org/articles/10.1051/m2an/2011077/
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