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G I Fann et al 2005 J. Phys.: Conf. Ser. 16 461 doi:10.1088/1742-6596/16/1/062

MRA and low-separation rank approximation with applications to quantum electronics structures computations

G I Fann1, R J Harrison2 and G Beylkin3

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Abstract References
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Alpert B 1993 A class of bases in L2 for the sparse representation of integral operators SIAM J. Math. Anal 24 (1) 246-62
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Alpert B, G Beylkin, D Gines and L Vozovoi 2002 Adaptive solution of partial differential equations in multiwavelet bases J. Comput. Phys. 182 (1) 149-90
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Beylkin G, R Coifman and V Rokhlin 1991 Fast wavelet transforms and numerical algorithms I Commun. Pure Appl. Math. 44 (2) 141-83
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1989 Yale Univ. Technical Report YALEU/DCS/RR-696 August 1989

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Beylkin G, R Coifman and V Rokhlin 1992 Wavelets in numerical analysis Wavelets and Their Applications (Jones and Bartlett, Boston, MA) p 181-210

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Beylkin G, R Cramer, G I Fann and R J Harrison 2004 Multiresolution separated representations of singular and weakly singular operators submitted

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Beylkin G and M J Mohlenkamp 2002 Numerical operator calculus in higher dimensions Proc. Natl. Acad. Sci. USA 99 (16) 10246-51
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http://www.pnas.org/cgi/content/abstract/112329799v1

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Beylkin G and M J Mohlenkamp 2004 Algorithms for numerical analysis in high dimensions SIAM J. Sci. Comput. accepted, APPM preprint #519, Univ. of Colorado http://amath.colorado.edu/pub/wavelets/papers/BEY-MOH2004P.pdf

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Beylkin G and L Monz'on 2005 On approximation of functions by exponential sums Appl. Comput. Harmon. Anal. 19 (1) 17-48
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Boys S F 1960 The integral formulae for the variational solution of the molecular many-electron wave equations in terms of Gaussian functions with direct electronic correlation Proc. R. Soc. London A 258 (1294) 402
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Cheng H, L Greengard and V Rokhlin 1999 A fast adaptive multipole algorithm in three dimensions J. Comput. Phys. 155 (2) 468-98
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Fann G I, G Beylkin, R J Harrison and K Jordan 2004 Singular operators in multiwavelet bases IBM J. Res. Dev. 48 (2) 161-71
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Harrison R J, G I Fann, T Yanai and G Beylkin 2003 Multiresolution quantum chemistry in multiwavelet bases Computational Sci.-ICCS 2003, Lecture Notes Comput. Sci. 2660 ed P M A Sloot et al (Springer) 103-110
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Harrison R J, G I Fann, T Yanai, Z Gan and G Beylkin 2004 Multiresolution quantum chemistry: basic theory and initial applications J. Chem. Phys. 121 (23) 11587-98
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http://amath.colorado.edu/pub/wavelets/papers/mrqc.pdf

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Kutzelnigg W 1994 Theory of the expansion of wave functions in a Gaussian basis Int. J. Quantum Chem. 51 447-63
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Longstaff J V L and K Singer 1960 The use of Gaussian (exponential quadratic) wave functions in molecular problems. II. Wave functions for the ground state of the hydrogen atom and of hydrogen molecule Proc. R. Soc. London A 258 (1294) 421
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Singer K 1960 The use of Gaussian (exponential quadratic) wave functions in molecular problems. I. General formulae for the evaluation of integrals Proc. R. Soc. London A 258 (1294) 412
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Yanai T, G I Fann, Z Gan, R J Harrison and G Beylkin 2004 Multiresolution quantum chemistry: Analytic derivatives for Hartree-Fock and density functional theory J. Chem. Phys. 121 (7) 2866-76
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Yanai T, G I Fann, Z Gan, R J Harrison and G Beylkin 2004 Multiresolution quantum chemistry: Hartree-Fock exchange J. Chem. Phys. 121 (14) 6680-88
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