Best N-term approximation in electronic structure calculations.I. One-electron reduced density matrix
Heinz-Jürgen Flad, Wolfgang Hackbusch, and Reinhold Schneider
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Submission date: 16. Jun. 2005
published in: ESAIM / Mathematical modelling and numerical analysis, 40 (2006) 1, p. 49-61
DOI number (of the published article): 10.1051/m2an:2006007
MSC-Numbers: 41A50, 41A63, 65Z05, 81V70
Keywords and phrases: best n-term approximation, wavelets, Hartree-Fock method, Density functional theory
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We discuss best N-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.