메뉴 건너뛰기




Volumn 5, Issue 3, 2007, Pages 523-550

Low rank Tucker-type tensor approximation to classical potentials

Author keywords

Classical potentials; Kronecker products; Multi dimensional integral operators; Multivariate functions; Tucker decomposition

Indexed keywords


EID: 34447513756     PISSN: 18951074     EISSN: 16443616     Source Type: Journal    
DOI: 10.2478/s11533-007-0018-0     Document Type: Article
Times cited : (75)

References (33)
  • 1
    • 24944569435 scopus 로고    scopus 로고
    • MATLAB tensor classes for fast algorithm prototyping
    • SANDIA Report, SAND2004-5187, Sandia National Laboratories
    • B.W. Bader and T.G. Kolda: MATLAB tensor classes for fast algorithm prototyping. SANDIA Report, SAND2004-5187, Sandia National Laboratories, 2004.
    • (2004)
    • Bader, B.W.1    Kolda, T.G.2
  • 2
    • 0036679114 scopus 로고    scopus 로고
    • "Numerical operator calculus in higher dimensions"
    • G. Beylkin and M. M. Mohlenkamp: "Numerical operator calculus in higher dimensions", PNAS, Vol. 99, (2002), pp. 10246-10251.
    • (2002) PNAS , vol.99 , pp. 10246-10251
    • Beylkin, G.1    Mohlenkamp, M.M.2
  • 3
    • 34250499792 scopus 로고
    • "Analysis of individual differences in multidimensional scaling via an N -way generalization of 'Eckart-Young' decomposition"
    • J.D. Carrol and J. Chang: "Analysis of individual differences in multidimensional scaling via an N -way generalization of 'Eckart-Young' decomposition", Psychometrika, Vol. 35, (1970), pp. 283-319.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carrol, J.D.1    Chang, J.2
  • 6
    • 17444379662 scopus 로고    scopus 로고
    • "Computation of the canonical decomposition by means of a simultaneous generalised Schur decomposition"
    • L. De Lathauwer, B. De Moor and J. Vandewalle: "Computation of the canonical decomposition by means of a simultaneous generalised Schur decomposition", SIAM J. Matrix Anal. Appl., Vol. 26, (2004) pp. 295-327.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 295-327
    • De Lathauwer, L.1    De Moor, B.2    Vandewalle, J.3
  • 7
    • 33746356349 scopus 로고    scopus 로고
    • "A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalisation"
    • L. De Lathauwer: "A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalisation", SIAM J. Matrix Anal. Appl., Vol. 28, (2006), pp. 642-666.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 642-666
    • De Lathauwer, L.1
  • 8
    • 34447543536 scopus 로고    scopus 로고
    • Decomposition of a higher-order tensor in block terms. Part II: Definitions and uniqueness
    • Tech. Report no. 07-81, ESAT/SCD/SISTA, K.U. Leuven, Belgium
    • L. De Lathauwer: Decomposition of a higher-order tensor in block terms. Part II: Definitions and uniqueness. Tech. Report no. 07-81, ESAT/SCD/ SISTA, K.U. Leuven, Belgium, 2007.
    • (2007)
    • De Lathauwer, L.1
  • 9
    • 34447551264 scopus 로고    scopus 로고
    • Concept of datasparse tensor-product approximation in many-particle models
    • Leipzig-Kiel (in preparation)
    • H.-J. Flad, W. Hackbusch, B.N. Khoromskij and R. Schneider: Concept of datasparse tensor-product approximation in many-particle models, Leipzig-Kiel, 2006 (in preparation).
    • (2006)
    • Flad, H.-J.1    Hackbusch, W.2    Khoromskij, B.N.3    Schneider, R.4
  • 10
    • 17144410769 scopus 로고    scopus 로고
    • "Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions"
    • I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij: "Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions", Computing, Vol. 74, (2005), pp. 131-157.
    • (2005) Computing , vol.74 , pp. 131-157
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 12
    • 34447531424 scopus 로고    scopus 로고
    • "Fast and exact projected convolution for non-equidistant grids"
    • Preprint: 102, MPI MIS, Leipzig
    • W. Hackbusch: "Fast and exact projected convolution for non-equidistant grids", Preprint: 102, MPI MIS, Leipzig 2006.
    • (2006)
    • Hackbusch, W.1
  • 13
    • 29144513721 scopus 로고    scopus 로고
    • "Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multivariate functions"
    • W. Hackbusch and B.N. Khoromskij: "Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multivariate functions", Computing, Vol. 76, (2006), pp. 177-202.
    • (2006) Computing , vol.76 , pp. 177-202
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 14
    • 29144481646 scopus 로고    scopus 로고
    • "Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part II. HKT representations of certain operators"
    • W. Hackbusch and B.N. Khoromskij: "Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part II. HKT representations of certain operators", Computing, Vol. 76, (2006), pp. 203-225.
    • (2006) Computing , vol.76 , pp. 203-225
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 15
    • 21244436795 scopus 로고    scopus 로고
    • "Hierarchical Kronecker tensor-product approximations"
    • W. Hackbusch, B.N. Khoromskij and E.E. Tyrtyshnikov: "Hierarchical Kronecker tensor-product approximations", J. Numer. Math., Vol. 13, (2005), pp. 119-156.
    • (2005) J. Numer. Math. , vol.13 , pp. 119-156
    • Hackbusch, W.1    Khoromskij, B.N.2    Tyrtyshnikov, E.E.3
  • 16
    • 34447528323 scopus 로고    scopus 로고
    • "Approximate Iterations for Structured Matrices"
    • Preprint: 112, MPI MIS, Leipzig 2005 (Numer. Math., submitted)
    • W. Hackbusch, B.N. Khoromskij and E.E. Tyrtyshnikov: "Approximate Iterations for Structured Matrices", Preprint: 112, MPI MIS, Leipzig 2005 (Numer. Math., submitted).
    • Hackbusch, W.1    Khoromskij, B.N.2    Tyrtyshnikov, E.E.3
  • 17
    • 0002740437 scopus 로고
    • "Foundation of the PARAFAC procedure: Model and conditions for an "explanatory" multi-mode factor analysis"
    • R. Harshman: "Foundation of the PARAFAC procedure: Model and conditions for an "explanatory" multi-mode factor analysis", UCLA Working Papers in Phonetics, Vol. 16, (1970), pp. 1-84.
    • (1970) UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.1
  • 18
    • 34447551262 scopus 로고    scopus 로고
    • "Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation"
    • B.N. Khoromskij: "Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation", Math. Comp., Vol. 76, (2007), pp. 1275-1290.
    • (2007) Math. Comp. , vol.76 , pp. 1275-1290
    • Khoromskij, B.N.1
  • 19
    • 34447551263 scopus 로고    scopus 로고
    • "An introduction to structured tensor-product representation of discrete nonlocal operators"
    • B.N. Khoromskij: "An introduction to structured tensor-product representation of discrete nonlocal operators", Lecture Notes MPI MIS Leipzig, Vol. 27, (2005).
    • (2005) Lecture Notes MPI MIS Leipzig , vol.27
    • Khoromskij, B.N.1
  • 21
    • 0036055687 scopus 로고    scopus 로고
    • "Orthogonal tensor decompositions"
    • T. Kolda: "Orthogonal tensor decompositions" SIAM J. Matrix Anal. Appl., Vol. 23, (2001), pp. 243-255.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 243-255
    • Kolda, T.1
  • 22
    • 48749101457 scopus 로고
    • "Three-way arrays: Rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics"
    • J.B. Kruskal: "Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics", Linear Algebra Appl., Vol. 18, (1977), pp. 95-138.
    • (1977) Linear Algebra Appl. , vol.18 , pp. 95-138
    • Kruskal, J.B.1
  • 23
    • 0002332422 scopus 로고
    • "Principal component analysis of three-mode data by means of alternating least squares algorithms"
    • P.M. Kroonenberg and J. De Leeuw: "Principal component analysis of three-mode data by means of alternating least squares algorithms", Psychometrika, Vol. 45, (1980), pp. 69-97.
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenberg, P.M.1    De Leeuw, J.2
  • 24
    • 14944376375 scopus 로고    scopus 로고
    • "On variational approximations in quantum molecular dynamics"
    • Ch. Lubich: "On variational approximations in quantum molecular dynamics", Math. Comp. Vol. 74, (2005), pp. 765-779.
    • (2005) Math. Comp. , vol.74 , pp. 765-779
    • Lubich, Ch.1
  • 26
    • 0033653594 scopus 로고    scopus 로고
    • "On the uniqueness of multilinear decomposition of N -way arrays"
    • N.D. Sidiropoulos and R. Bro: "On the uniqueness of multilinear decomposition of N -way arrays", Journal of Chemometrics, Vol. 14, (2000), 229-239.
    • (2000) Journal of Chemometrics , vol.14 , pp. 229-239
    • Sidiropoulos, N.D.1    Bro, R.2
  • 27
    • 33750991900 scopus 로고    scopus 로고
    • "On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition"
    • A. Stegeman and N.D. Sidiropoulos: "On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition", Lin. Alg. Appl., Vol. 420, (2007), pp. 540-552.
    • (2007) Lin. Alg. Appl. , vol.420 , pp. 540-552
    • Stegeman, A.1    Sidiropoulos, N.D.2
  • 30
    • 0033130204 scopus 로고    scopus 로고
    • "Greedy Algorithms and M-Term Approximation with Regard to Redundant Dictionaries"
    • V.N. Temlyakov: "Greedy Algorithms and M-Term Approximation with Regard to Redundant Dictionaries", J. of Approx. Theory, Vol. 98, (1999), pp. 117-145.
    • (1999) J. of Approx. Theory , vol.98 , pp. 117-145
    • Temlyakov, V.N.1
  • 31
    • 0013953617 scopus 로고
    • "Some mathematical notes on three-mode factor analysis"
    • L.R. Tucker: "Some mathematical notes on three-mode factor analysis", Psychometrika, Vol. 31, (1966), pp. 279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 32
    • 0142055272 scopus 로고    scopus 로고
    • "Tensor approximations of matrices generated by asymptotically smooth functions"
    • (translated from Mat. Sb., Vol. 194, (2003), pp. 146-160)
    • E.E. Tyrtyshnikov: "Tensor approximations of matrices generated by asymptotically smooth functions", Sb. Math+., Vol. 194, (2003), pp. 941-954 (translated from Mat. Sb., Vol. 194, (2003), pp. 146-160).
    • (2003) Sb. Math+. , vol.194 , pp. 941-954
    • Tyrtyshnikov, E.E.1
  • 33
    • 0036056838 scopus 로고    scopus 로고
    • "Rank-0ne approximation to high order tensors"
    • T. Zang and G. Golub: "Rank-0ne approximation to high order tensors", SIAM J. Matrix Anal. Appl., Vol. 23, (2001), pp. 534-550.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 534-550
    • Zang, T.1    Golub, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.