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Volumn , Issue , 2009, Pages 39-74

On the efficient computation of high-dimensional integrals and the approximation by exponential sums

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EID: 84892819022     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-03413-8_3     Document Type: Chapter
Times cited : (66)

References (32)
  • 1
    • 0001277795 scopus 로고
    • Elimination of energy denominators in Møller-Plesset perturbation theory by a Laplace transform approach
    • J. Almlöf: Elimination of energy denominators in Møller-Plesset perturbation theory by a Laplace transform approach. Chem. Phys. Lett. 176 (.1991), 319-320
    • (1991) Chem. Phys. Lett , vol.176 , pp. 319-320
    • Almlöf, J.1
  • 2
    • 0000277432 scopus 로고    scopus 로고
    • Linear scaling second-order Moller-Plesset theory in the atomic orbital basis for large molecular systems
    • P.Y. Ayala and G. Scuseria: Linear scaling second-order Moller-Plesset theory in the atomic orbital basis for large molecular systems. J. Chem. Phys. 110 (.1999), 3660
    • (1999) J. Chem. Phys , vol.110 , pp. 3660
    • Ayala, P.Y.1    Scuseria, G.2
  • 5
    • 49049138726 scopus 로고
    • On the conjecture of meinardus on the rational approximation of ex
    • D. Braess: On the conjecture of Meinardus on the rational approximation of ex. J. Approximation Theory 36 (.1982), 317-320
    • (1982) J. Approximation Theory , vol.36 , pp. 317-320
    • Braess, D.1
  • 6
    • 24344506306 scopus 로고
    • Asymptotics for the approximation of wave functions by exponential sums
    • D. Braess: Asymptotics for the approximation of wave functions by exponential sums. J. Approximation Theory 83 (.1995), 93-103
    • (1995) J. Approximation Theory , vol.83 , pp. 93-103
    • Braess, D.1
  • 7
    • 26444558083 scopus 로고    scopus 로고
    • Approximation of 1/x by exponential sums in [18)
    • D. Braess and W. Hackbusch: Approximation of 1/x by exponential sums in [1,8). IMA J. Numer. Anal. 25 (.2005), 685-697
    • (2005) IMA J Numer Anal , vol.25 , pp. 685-697
    • Braess, D.1    Hackbusch, W.2
  • 9
    • 44949197681 scopus 로고    scopus 로고
    • Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems
    • A.F. Izmaylov and G.E. Scuseria: Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems. Phys. Chem. Chem. Phys. 10 (.2008), 3421-3429
    • (2008) Phys. Chem. Chem. Phys , vol.10 , pp. 3421-3429
    • Izmaylov, A.F.1    Scuseria, G.E.2
  • 10
    • 10844228090 scopus 로고    scopus 로고
    • Scaled opposite-spin second order Møller-Plesset correlation energy: An economical electronic structure method
    • Y. Jung, R.C. Lochan, A.D. Dutoi, and M. Head-Gordon: Scaled opposite-spin second order Møller-Plesset correlation energy: An economical electronic structure method. J. Chem. Phys. 121 (.2004), 9793
    • (2004) J. Chem. Phys , vol.121 , pp. 9793
    • Jung, Y.1    Lochan, R.C.2    Dutoi, A.D.3    Head-Gordon, M.4
  • 11
    • 3042756404 scopus 로고    scopus 로고
    • Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
    • L. Grasedyck: Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure. Computing, 72 (.2004), 247-265
    • (2004) Computing , vol.72 , pp. 247-265
    • Grasedyck, L.1
  • 12
    • 29144489004 scopus 로고    scopus 로고
    • Approximation of 1/x-y by exponentials for wavelet applications
    • W. Hackbusch: Approximation of 1/x-y by exponentials for wavelet applications. Computing, 76 (.2006), 359-366
    • (2006) Computing , vol.76 , pp. 359-366
    • Hackbusch, W.1
  • 13
    • 52949104402 scopus 로고    scopus 로고
    • Efficient convolution with the Newton potential in d dimensions
    • W. Hackbusch: Efficient convolution with the Newton potential in d dimensions. Numer.Math. 110 (.2008), 449-489
    • (2008) Numer.Math , vol.110 , pp. 449-489
    • Hackbusch, W.1
  • 15
    • 36449001643 scopus 로고
    • Laplace transform techniques inMøller-Plesset perturbation theory
    • M. Häser and J. Almlöf: Laplace transform techniques inMøller-Plesset perturbation theory. J. Chem. Phys. 96 (.1992), 489
    • (1992) J. Chem. Phys , vol.96 , pp. 489
    • Häser, M.1    Almlöf, J.2
  • 16
    • 0002747967 scopus 로고
    • Møller-Plesset (.MP2) perturbation theory for large molecules
    • M. Häser: Møller-Plesset (.MP2) perturbation theory for large molecules. Theor. Chim. Acta 87 (.1993), 147-173
    • (1993) Theor. Chim. Acta , vol.87 , pp. 147-173
    • Häser, M.1
  • 17
    • 33344456194 scopus 로고    scopus 로고
    • Implementation of Surj́an's density matrix formulae for calculating second-order Møller-Plesset energy
    • M. Kobayashi and H. Nakai: Implementation of Surj́an's density matrix formulae for calculating second-order Møller-Plesset energy. Chem. Phys. Lett. 420 (.2006), 250-255
    • (2006) Chem. Phys. Lett , vol.420 , pp. 250-255
    • Kobayashi, M.1    Nakai, H.2
  • 18
    • 84987143342 scopus 로고
    • Theory of the expansion of wave functions in a Gaussian basis
    • W. Kutzelnigg: Theory of the expansion of wave functions in a Gaussian basis. Int. J. of Quantum Chemistry 51 (.1994), 447-463
    • (1994) Int. J. of Quantum Chemistry , vol.51 , pp. 447-463
    • Kutzelnigg, W.1
  • 19
    • 27644470116 scopus 로고    scopus 로고
    • Rigorous integral screening for electron correlation methods
    • D.S. Lambrecht, B. Doser, and C. Ochsenfeld: Rigorous integral screening for electron correlation methods. J. Chem. Phys. 123 (.2005), 184102
    • (2005) J. Chem. Phys , vol.123 , pp. 184102
    • Lambrecht, D.S.1    Doser, B.2    Ochsenfeld, C.3
  • 20
    • 0007285240 scopus 로고
    • Rational approximation to ex
    • D.J. Newman: Rational approximation to ex. J. Approximation Theory 27 (.1979), 234-235
    • (1979) J. Approximation Theory , vol.27 , pp. 234-235
    • Newman, D.J.1
  • 21
    • 21644454871 scopus 로고
    • Sur un proćed́e convergent d'approximations successives pour d́eterminer les polyn̂omes d'approximation
    • E.J. Remez: Sur un proćed́e convergent d'approximations successives pour d́eterminer les polyn̂omes d'approximation. Compt. Rend. Acad. Sc. 198 (.1934), 2063-2065
    • (1934) Compt. Rend. Acad. Sc. , vol.198 , pp. 2063-2065
    • Remez, E.J.1
  • 22
    • 26444522849 scopus 로고
    • Betrachtungen zur Quadratwurzeliteration
    • R. Rutishauser: Betrachtungen zur Quadratwurzeliteration. Monatshefte Math. 67 (.1963), 452-464
    • (1963) Monatshefte Math , vol.67 , pp. 452-464
    • Rutishauser, R.1
  • 23
    • 44949246345 scopus 로고    scopus 로고
    • On the use of the Laplace transform in local correlation methods
    • DOI: 10.1039/b802993h
    • D. Kats, D. Usvyat and M. Schütz: On the use of the Laplace transform in local correlation methods. Phys. Chem. Chem. Phys., 2008, DOI: 10.1039/b802993h
    • Phys. Chem. Chem. Phys , vol.2008
    • Kats, D.1    Usvyat, D.2    Schütz, M.3
  • 24
    • 42449083402 scopus 로고    scopus 로고
    • An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory
    • S. Schweizer, B. Doser, and C. Ochsenfeld: An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory. J. Chem. Phys. 128 (.2008), 154101
    • (2008) J Chem Phys , vol.128 , pp. 154101
    • Schweizer, S.1    Doser, B.2    Ochsenfeld, C.3
  • 25
    • 0141543757 scopus 로고    scopus 로고
    • Best uniform rational approximation of x?ön 0 1
    • H.R. Stahl: Best uniform rational approximation of x?ön [0,1]. Acta Math. 190 (.2003), 241- 306
    • (2003) Acta Math , vol.190 , pp. 241-306
    • Stahl, H.R.1
  • 27
    • 16644362781 scopus 로고    scopus 로고
    • The MP2 energy as a functional of the Hartree-Fock density matrix
    • P.R. Surj́an: The MP2 energy as a functional of the Hartree-Fock density matrix. Chem. Phys. Lett. 406 (.2005), 318-320
    • (2005) Chem. Phys. Lett , vol.406 , pp. 318-320
    • Surj́an, P.R.1
  • 28
    • 49149096624 scopus 로고    scopus 로고
    • Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller-Plesset perturbation theories
    • A. Takatsuka, S. Ten-no, andW. Hackbusch: Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller- Plesset perturbation theories. J. Chem. Phys. 129 (.2008), 044112
    • (2008) J. Chem. Phys , vol.129 , pp. 044112
    • Takatsuka, A.1    Ten-No, S.2    Hackbusch, W.3
  • 29
    • 26444487952 scopus 로고
    • On the Least Deviation of the Function Signx and Its Primitives from the Rational Functions in the Lp Metrics 0 < P < 8
    • N.S. Vjäceslavov: On the least deviation of the function signx and its primitives from the rational functions in the Lp metrics, 0 < p < 8. Math. USSR Sbornik 32 (.1977), 19-31
    • (1977) Math. USSR Sbornik , vol.32 , pp. 19-31
    • Vjäceslavov, N.S.1
  • 30
    • 0041610113 scopus 로고    scopus 로고
    • Møller-Plesset correlation energies in a localized orbital basis using a Laplace transform technique
    • A.K. Wilson and J. Almlöf: Møller-Plesset correlation energies in a localized orbital basis using a Laplace transform technique. Theor. Chim. Acta 95 (.1997), 49-62
    • (1997) Theor. Chim. Acta , vol.95 , pp. 49-62
    • Wilson, A.K.1    Almlöf, J.2
  • 31
    • 84892789200 scopus 로고    scopus 로고
    • Webpages www.mis.mpg.de/scicomp/EXP SUM/1 x/ and ldots/1 sqrtx/ with explanations in .../1 x/tabelle and .../1 sqrtx/tabelle
    • Webpages
  • 32
    • 0013259808 scopus 로고
    • Application of elliptic functions to questions of functions deviating least and most from zero
    • Russian St. Petersburg 30 reprinted in collected works II 1-59 Izdat, Akad. Nauk SSSR, Moscow 1932
    • E.I. Zolotarov: Application of elliptic functions to questions of functions deviating least and most from zero (.Russian). Zap. Imp. Akad. Nauk (.1877). St. Petersburg 30 no. 5; reprinted in collected works II, pp. 1-59. Izdat, Akad. Nauk SSSR, Moscow 1932
    • (1877) Zap. Imp. Akad. Nauk , vol.5
    • Zolotarov, E.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.