We discuss best -term approximation spaces for one-electron wavefunctions and reduced density matrices emerging from Hartree-Fock and density functional theory. The approximation spaces for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted spaces of wavelet coefficients to proof that both and are in for all with . Our proof is based on the assumption that the possess an asymptotic smoothness property at the electron-nuclear cusps.
Mots-clés : best $N$-term approximation, wavelets, Hartree-Fock method, density functional theory
@article{M2AN_2006__40_1_49_0,
author = {Flad, Heinz-J\"urgen and Hackbusch, Wolfgang and Schneider, Reinhold},
title = {Best $N$-term approximation in electronic structure calculations {I.} {One-electron} reduced density matrix},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {49--61},
publisher = {EDP-Sciences},
volume = {40},
number = {1},
year = {2006},
doi = {10.1051/m2an:2006007},
mrnumber = {2223504},
zbl = {1100.81050},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006007/}
}
TY - JOUR AU - Flad, Heinz-Jürgen AU - Hackbusch, Wolfgang AU - Schneider, Reinhold TI - Best $N$-term approximation in electronic structure calculations I. One-electron reduced density matrix JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 49 EP - 61 VL - 40 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006007/ DO - 10.1051/m2an:2006007 LA - en ID - M2AN_2006__40_1_49_0 ER -
%0 Journal Article %A Flad, Heinz-Jürgen %A Hackbusch, Wolfgang %A Schneider, Reinhold %T Best $N$-term approximation in electronic structure calculations I. One-electron reduced density matrix %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 49-61 %V 40 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006007/ %R 10.1051/m2an:2006007 %G en %F M2AN_2006__40_1_49_0
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold. Best $N$-term approximation in electronic structure calculations I. One-electron reduced density matrix. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 1, pp. 49-61. doi : 10.1051/m2an:2006007. http://www.numdam.org/articles/10.1051/m2an:2006007/
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