메뉴 건너뛰기




Volumn 17, Issue 6, 2010, Pages 935-952

Cross approximation in tensor electron density computations

Author keywords

Canonical decomposition; Cross approximation; Electron density; Hartree Fock Kohn Sham; Tucker approximation

Indexed keywords


EID: 78649667629     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.682     Document Type: Article
Times cited : (23)

References (33)
  • 1
    • 0142055272 scopus 로고    scopus 로고
    • Tensor approximations of matrices generated by asymptotically smooth functions
    • DOI: 10.1070/SM2003v194n06ABEH000747.
    • Tyrtyshnikov EE. Tensor approximations of matrices generated by asymptotically smooth functions. Sbornik: Mathematics 2003; 194(6):941-954. DOI: 10.1070/SM2003v194n06ABEH000747.
    • (2003) Sbornik: Mathematics , vol.194 , Issue.6 , pp. 941-954
    • Tyrtyshnikov, E.E.1
  • 2
    • 0742320626 scopus 로고    scopus 로고
    • Kronecker-product approximations for some function-related matrices
    • DOI: 10.1016/j.laa.2003.08.013.
    • Tyrtyshnikov EE. Kronecker-product approximations for some function-related matrices. Linear Algebra and its Applications 2004; 379:423-437. DOI: 10.1016/j.laa.2003.08.013.
    • (2004) Linear Algebra and its Applications , vol.379 , pp. 423-437
    • Tyrtyshnikov, E.E.1
  • 4
    • 0036391742 scopus 로고    scopus 로고
    • Application of the three-way decomposition for matrix compression
    • DOI: 10.1002/nla.297.
    • Ibraghimov I. Application of the three-way decomposition for matrix compression. Numerical Linear Algebra with Applications 2002; 9(6-7):551-565. DOI: 10.1002/nla.297.
    • (2002) Numerical Linear Algebra with Applications , vol.9 , Issue.6-7 , pp. 551-565
    • Ibraghimov, I.1
  • 5
    • 27644573654 scopus 로고    scopus 로고
    • Approximate inversion of matrices in the process of solving a hypersingular integral equation
    • Oseledets IV, Tyrtyshnikov EE. Approximate inversion of matrices in the process of solving a hypersingular integral equation. Computational Mathematics and Mathematical Physics 2005; 45(2):302-313.
    • (2005) Computational Mathematics and Mathematical Physics , vol.45 , Issue.2 , pp. 302-313
    • Oseledets, I.V.1    Tyrtyshnikov, E.E.2
  • 6
    • 78649646365 scopus 로고    scopus 로고
    • Polilinear approximation of matrices and integral equations. Ph.D. Thesis, INM RAS, Moscow, Available from: (in Russian).
    • Savostyanov DV. Polilinear approximation of matrices and integral equations. Ph.D. Thesis, INM RAS, Moscow, 2006. Available from: (in Russian).
    • (2006)
    • Savostyanov, D.V.1
  • 7
    • 11044224123 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry: basic theory and initial applications
    • DOI: 10.1063/1.1791051.
    • Beylkin G, Fann G, Gan Z, Harrison R, Yanai T. Multiresolution quantum chemistry: basic theory and initial applications. Journal of Chemical Physics 2004; 121(23):11587-11598. DOI: 10.1063/1.1791051.
    • (2004) Journal of Chemical Physics , vol.121 , Issue.23 , pp. 11587-11598
    • Beylkin, G.1    Fann, G.2    Gan, Z.3    Harrison, R.4    Yanai, T.5
  • 10
    • 47849118953 scopus 로고    scopus 로고
    • On tensor approximation of Green iterations for Kohn-Sham equations
    • DOI: 10.1007/s00791-008-0097-x.
    • Khoromskij BN. On tensor approximation of Green iterations for Kohn-Sham equations. Computing and Visualization in Science 2008; 11(4-6):259-271. DOI: 10.1007/s00791-008-0097-x.
    • (2008) Computing and Visualization in Science , vol.11 , Issue.4-6 , pp. 259-271
    • Khoromskij, B.N.1
  • 11
    • 67649378419 scopus 로고    scopus 로고
    • Tensor decomposition in electronic structure calculations on 3D Cartesian grids
    • DOI: 10.1016/j.jcp.2009.04.043
    • Chinnamsetty SR, Flad HJ, Khoromskaia V, Khoromskij BN. Tensor decomposition in electronic structure calculations on 3D Cartesian grids. Journal of Computational Physics 2009; 228(16):5749-5762. DOI: 10.1016/j.jcp.2009.04.043.
    • (2009) Journal of Computational Physics , vol.228 , Issue.16 , pp. 5749-5762
    • Chinnamsetty, S.R.1    Flad, H.J.2    Khoromskaia, V.3    Khoromskij, B.N.4
  • 12
    • 84897586218 scopus 로고    scopus 로고
    • Multigrid accelerated tensor approximation of function related multidimensional arrays
    • DOI: 10.1137/080730408.
    • Khoromskij BN, Khoromskaia V. Multigrid accelerated tensor approximation of function related multidimensional arrays. SIAM Journal on Scientific Computing 2009; 31(4):3002-3026. DOI: 10.1137/080730408.
    • (2009) SIAM Journal on Scientific Computing , vol.31 , Issue.4 , pp. 3002-3026
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 13
    • 78649662406 scopus 로고    scopus 로고
    • Fast and accurate tensor approximation of multivariate convolution with linear scaling in dimension. Preprint 36, MIS MPI, Available from
    • Khoromskij BN. Fast and accurate tensor approximation of multivariate convolution with linear scaling in dimension. Preprint 36, MIS MPI, 2008. Available from:
    • (2008)
    • Khoromskij, B.N.1
  • 14
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • DOI: 10.1007/s006070070031.
    • Tyrtyshnikov EE. Incomplete cross approximation in the mosaic-skeleton method. Computing 2000; 64(4):367-380. DOI: 10.1007/s006070070031.
    • (2000) Computing , vol.64 , Issue.4 , pp. 367-380
    • Tyrtyshnikov, E.E.1
  • 15
    • 0037790752 scopus 로고    scopus 로고
    • The maximal-volume concept in approximation by low-rank matrices
    • Goreinov SA, Tyrtyshnikov EE. The maximal-volume concept in approximation by low-rank matrices. Contemporary Mathematics 2001; 208:47-51.
    • (2001) Contemporary Mathematics , vol.208 , pp. 47-51
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2
  • 17
    • 85162707890 scopus 로고
    • The expression of a tensor or a polyadic as a sum of products
    • Hitchcock FL. The expression of a tensor or a polyadic as a sum of products. Journal of Mathematical Physics 1927; 6(1):164-189.
    • (1927) Journal of Mathematical Physics , vol.6 , Issue.1 , pp. 164-189
    • Hitchcock, F.L.1
  • 18
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition
    • Caroll JD, Chang JJ. Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition. Psychometrika 1970; 35:283-319.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Caroll, J.D.1    Chang, J.J.2
  • 19
    • 0002740437 scopus 로고
    • Foundations of the Parafac procedure: models and conditions for an explanatory multimodal factor analysis. UCLA Working Papers in Phonetics
    • Harshman RA. Foundations of the Parafac procedure: models and conditions for an explanatory multimodal factor analysis. UCLA Working Papers in Phonetics 1970; 16:1-84.
    • (1970) , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 20
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • DOI: 10.1137/06066518x.
    • de Silva V, Lim L. Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM Journal on Matrix Analysis and Applications 2008; 30(3):1084-1127. DOI: 10.1137/06066518x.
    • (2008) SIAM Journal on Matrix Analysis and Applications , vol.30 , Issue.3 , pp. 1084-1127
    • de Silva, V.1    Lim, L.2
  • 21
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • Tucker LR. Some mathematical notes on three-mode factor analysis. Psychometrika 1966; 31:279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 23
    • 0011680262 scopus 로고
    • Pseudo-skeleton approximations of matrices. Reports of Russian Academy of Sciences
    • Goreinov SA, Tyrtyshnikov EE, Zamarashkin NL. Pseudo-skeleton approximations of matrices. Reports of Russian Academy of Sciences 1995; 342(2):151-152.
    • (1995) , vol.342 , Issue.2 , pp. 151-152
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2    Zamarashkin, N.L.3
  • 26
    • 0004236492 scopus 로고    scopus 로고
    • Matrix Computations
    • Johns Hopkins University Press: Baltimore, MD,
    • Golub G, Van Loan C. Matrix Computations. Johns Hopkins University Press: Baltimore, MD, 1996.
    • (1996)
    • Golub, G.1    Van Loan, C.2
  • 27
    • 68149178489 scopus 로고    scopus 로고
    • Linear algebra for tensor problems
    • DOI: 10.1007/s00607-009-0047-6.
    • Oseledets IV, Savostyanov DV, Tyrtyshnikov EE. Linear algebra for tensor problems. Computing 2009; 85(3):169-188. DOI: 10.1007/s00607-009-0047-6.
    • (2009) Computing , vol.85 , Issue.3 , pp. 169-188
    • Oseledets, I.V.1    Savostyanov, D.V.2    Tyrtyshnikov, E.E.3
  • 28
    • 5844381624 scopus 로고    scopus 로고
    • Approximation of boundary element matrices
    • DOI: 10.1007/pl00005410.
    • Bebendorf M. Approximation of boundary element matrices. Numerische Mathematik 2000; 86(4):565-589. DOI: 10.1007/pl00005410.
    • (2000) Numerische Mathematik , vol.86 , Issue.4 , pp. 565-589
    • Bebendorf, M.1
  • 29
    • 2942606241 scopus 로고    scopus 로고
    • Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems
    • DOI: 10.1137/s1064827503421689.
    • Ford JM, Tyrtyshnikov EE. Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems. SIAM Journal on Scientific Computing 2003; 25(3):961-981. DOI: 10.1137/s1064827503421689.
    • (2003) SIAM Journal on Scientific Computing , vol.25 , Issue.3 , pp. 961-981
    • Ford, J.M.1    Tyrtyshnikov, E.E.2
  • 30
    • 78649684489 scopus 로고    scopus 로고
    • Fast revealing of mode ranks of tensor in canonical formal
    • DOI: 10.4208/nmtma.2009.m9006s.
    • Savostyanov DV. Fast revealing of mode ranks of tensor in canonical formal. Numerical Mathematics: Theory, Methods and Applications 2009; 2(4):439-444. DOI: 10.4208/nmtma.2009.m9006s.
    • (2009) Numerical Mathematics: Theory, Methods and Applications , vol.2 , Issue.4 , pp. 439-444
    • Savostyanov, D.V.1
  • 31
    • 47049085255 scopus 로고    scopus 로고
    • On cross approximation of multi-index array
    • DOI: 10.1134/s106456240803023x.
    • Goreinov SA. On cross approximation of multi-index array. Doklady: Mathematics 2008; 420(4):404-406. DOI: 10.1134/s106456240803023x.
    • (2008) Doklady: Mathematics , vol.420 , Issue.4 , pp. 404-406
    • Goreinov, S.A.1
  • 32
    • 78649638507 scopus 로고    scopus 로고
    • Use of tensor formats in elliptic eigenvalue problems. Preprint 78, MIS MPI, Leipzig, Available from: .
    • Hackbusch W, Khoromskij BN, Sauter SA, Tyrtyshnikov EE. Use of tensor formats in elliptic eigenvalue problems. Preprint 78, MIS MPI, Leipzig, 2008. Available from:
    • (2008)
    • Hackbusch, W.1    Khoromskij, B.N.2    Sauter, S.A.3    Tyrtyshnikov, E.E.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.