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All issues Volume 40 / No 1 (January-February 2006) ESAIM: M2AN, 40 1 (2006) 49-61 References
Free Access
Issue
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
Page(s) 49 - 61
DOI https://doi.org/10.1051/m2an:2006007
Published online 23 February 2006
  1. D. Braess, Asymptotics for the approximation of wave functions by exponential sums. J. Approx. Theory 83 (1995) 93–103. [CrossRef] [MathSciNet] [Google Scholar]
  2. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numerica 13 (2004) 147–269. [Google Scholar]
  3. A. Cohen, R.A. DeVore and R. Hochmuth, Restricted nonlinear approximation. Constr. Approx. 16 (2000) 85–113. [CrossRef] [MathSciNet] [Google Scholar]
  4. R.A. DeVore, Nonlinear approximation. Acta Numerica 7 (1998) 51–150. [CrossRef] [Google Scholar]
  5. R.A. DeVore, B. Jawerth and V. Popov, Compression of wavelet decompositions. Amer. J. Math. 114 (1992) 737–785. [CrossRef] [MathSciNet] [Google Scholar]
  6. R.A. DeVore, S.V. Konyagin and V.N. Temlyakov, Hyperbolic wavelet approximation. Constr. Approx. 14 (1998) 1–26. [Google Scholar]
  7. H.-J. Flad, W. Hackbusch, D. Kolb and R. Schneider, Wavelet approximation of correlated wavefunctions. I. Basics. J. Chem. Phys. 116 (2002) 9641–9657. [CrossRef] [Google Scholar]
  8. H.-J. Flad, W. Hackbusch, H. Luo and D. Kolb, Diagrammatic multiresolution analysis for electron correlations. Phys. Rev. B. 71 (2005) 125115. [CrossRef] [Google Scholar]
  9. H.-J. Flad, W. Hackbusch, H. Luo and D. Kolb, Wavelet approach to quasi two-dimensional extended many-particle systems. I. supercell Hartree-Fock method. J. Comp. Phys. 205 (2005) 540–566. [CrossRef] [Google Scholar]
  10. S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Ostergaard S orensen, On the regularity of the density of electronic wavefunctions. Contemp. Math. 307 (2002) 143–148. [Google Scholar]
  11. S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Ostergaard S orensen, The electron density is smooth away from the nuclei. Commun. Math. Phys. 228 (2002) 401–415. [CrossRef] [Google Scholar]
  12. J. Garcke and M. Griebel, On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. J. Comp. Phys. 165 (2000) 694–716. [Google Scholar]
  13. A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper and J. Olsen, Basis-set convergence of the energy in molecular Hartree-Fock calculations. Chem. Phys. Lett. 302 (1999) 437–446. [CrossRef] [Google Scholar]
  14. R.J. Harrison, G.I. Fann, T. Yanai, Z. Gan and G. Beylkin, Multiresolution quantum chemistry: Basic theory and initial applications. J. Chem. Phys. 121 (2004) 11587–11598. [CrossRef] [PubMed] [Google Scholar]
  15. T. Helgaker, P. Jørgensen and J. Olsen, Molecular Electronic-Structure Theory, Wiley, New York (1999). [Google Scholar]
  16. R.N. Hill, Rates of convergence and error estimation formulas for the Rayleigh-Ritz variational method. J. Chem. Phys. 83 (1985) 1173–1196. [CrossRef] [Google Scholar]
  17. M. Hoffmann-Ostenhof and R. Seiler, Cusp conditions for eigenfunctions of n-electron systems, Phys. Rev. A 23 (1981) 21–23. [Google Scholar]
  18. M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and H. Stremnitzer, Local properties of Coulombic wave functions. Commun. Math. Phys. 163 (1994) 185–215. [CrossRef] [Google Scholar]
  19. M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Ostergaard S orensen, Electron wavefunctions and densities for atoms. Ann. Henri Poincaré 2 (2001) 77–100. [CrossRef] [MathSciNet] [Google Scholar]
  20. T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10 (1957) 151–177. [Google Scholar]
  21. W. Kutzelnigg, Theory of the expansion of wave functions in a Gaussian basis. Int. J. Quantum Chem. 51 (1994) 447–463. [CrossRef] [Google Scholar]
  22. W. Kutzelnigg and J.D. Morgan III, Rates of convergence of the partial-wave expansions of atomic correlation energies. J. Chem. Phys. 96 (1992) 4484–4508. [CrossRef] [Google Scholar]
  23. E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53 (1977) 185–194. [CrossRef] [MathSciNet] [Google Scholar]
  24. H. Luo, D. Kolb, H.-J. Flad, W. Hackbusch and T. Koprucki, Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes. J. Chem. Phys. 117 (2002) 3625–3638. [CrossRef] [Google Scholar]
  25. P.-A. Nitsche, Best N-term approximation spaces for sparse grids, Research Report No. 2003-11, Seminar für Angewandte Mathematik, ETH Zürich. [Google Scholar]
  26. R. Schneider, Multiskalen- und Wavelet-Matrixkompression, Teubner, Stuttgart (1998). [Google Scholar]
  27. T. Yanai, G.I. Fann, Z. Gan, R.J. Harrison and G. Beylkin, Multiresolution quantum chemistry in multiwavelet basis: Hartree-Fock exchange. J. Chem. Phys. 121 (2004) 6680–6688. [CrossRef] [PubMed] [Google Scholar]
  28. T. Yanai, G.I. Fann, Z. Gan, R.J. Harrison and G. Beylkin, Multiresolution quantum chemistry in multiwavelet basis: Analytic derivatives for Hartree-Fock and density functional theory. J. Chem. Phys. 121 (2004) 2866–2876. [CrossRef] [PubMed] [Google Scholar]
  29. H. Yserentant, On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math. 98 (2004) 731–759. [CrossRef] [MathSciNet] [Google Scholar]
  30. H. Yserentant, Sparse grid spaces for the numerical solution of the electronic Schrödinger equation. Numer. Math. 101 (2005) 381–389. [CrossRef] [MathSciNet] [Google Scholar]

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