메뉴 건너뛰기




Volumn 19, Issue 1, 2012, Pages 103-111

Fast truncation of mode ranks for bilinear tensor operations

Author keywords

Cross approximation; Fast compression; Multidimensional arrays; Structured tensors; Tucker approximation

Indexed keywords


EID: 84855214058     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.765     Document Type: Article
Times cited : (7)

References (29)
  • 1
    • 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
  • 2
    • 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
  • 3
    • 0002740437 scopus 로고
    • Foundations of the Parafac procedure: models and conditions for an explanatory multimodal factor analysis
    • 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) UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 4
    • 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
  • 5
    • 84855218694 scopus 로고    scopus 로고
    • Tensor decomposition: state of the art and applications. IMA Conference on Mathematics in Signal Processing, Warwick, U.K.
    • Comon P. Tensor decomposition: state of the art and applications. IMA Conference on Mathematics in Signal Processing, Warwick, U.K., 2000.
    • (2000)
    • Comon, P.1
  • 7
    • 70449522299 scopus 로고    scopus 로고
    • Black box low tensor rank approximation using fibre-crosses
    • DOI: 10.1007/s00365-009-9076-9.
    • Espig M, Grasedick L, Hackbusch W. Black box low tensor rank approximation using fibre-crosses. Constructive Approximation 2009; 30(3):557-597. DOI: 10.1007/s00365-009-9076-9.
    • (2009) Constructive Approximation , vol.30 , Issue.3 , pp. 557-597
    • Espig, M.1    Grasedick, L.2    Hackbusch, W.3
  • 9
    • 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
  • 10
    • 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
  • 12
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least squares algorithms
    • Kroonenberg P, de Leeuw J. Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 1980; 45(1):69-97.
    • (1980) Psychometrika , vol.45 , Issue.1 , pp. 69-97
    • Kroonenberg, P.1    de Leeuw, J.2
  • 16
    • 78649684489 scopus 로고    scopus 로고
    • Fast revealing of mode ranks of tensor in canonical format
    • DOI: 10.4208/nmtma.2009.m9006s.
    • Savostyanov DV. Fast revealing of mode ranks of tensor in canonical format. 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
  • 19
    • 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
  • 20
    • 84855225002 scopus 로고
    • A good submatrix is hard to find, School of industrial and systems engineering, Georgia Institute of Technology
    • Bartholdi JJ. A good submatrix is hard to find, School of industrial and systems engineering, Georgia Institute of Technology, 1982.
    • (1982)
    • Bartholdi, J.J.1
  • 21
    • 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
  • 24
    • 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
  • 25
    • 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
  • 26
    • 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
  • 29
    • 84855218693 scopus 로고    scopus 로고
    • Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case. Preprint 2010-01, INM RAS, Moscow, Available from:
    • Goreinov SA, Oseledets IV, Savostyanov DV. Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case. Preprint 2010-01, INM RAS, Moscow, 2010. Available from:
    • (2010)
    • Goreinov, S.A.1    Oseledets, I.V.2    Savostyanov, D.V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.