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.

We discuss best N-term approximation spaces for one-electron wavefunctions φ i and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces A q α (H 1 ) 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 q spaces of wavelet coefficients to proof that both φ i and ρ are in A q α (H 1 ) for all α>0 with α=1 q-1 2. Our proof is based on the assumption that the φ i possess an asymptotic smoothness property at the electron-nuclear cusps.

DOI : 10.1051/m2an:2006007
Classification : 41A50, 41A63, 65Z05, 81V70
Mots clés : best $N$-term approximation, wavelets, Hartree-Fock method, density functional theory
Flad, Heinz-Jürgen  ; Hackbusch, Wolfgang  ; Schneider, Reinhold 1

1 Institut für Informatik Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. ; Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany.
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     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},
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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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