메뉴 건너뛰기




Volumn 438, Issue 2, 2013, Pages 639-657

Black box approximation of tensors in hierarchical Tucker format

Author keywords

Cross approximation; Hierarchical Tucker; Tensor approximation; Tensor rank; Tensor train

Indexed keywords

ADAPTIVE APPROACH; APPROXIMABILITY; BLACK BOXES; CROSS APPROXIMATION; ERROR BOUND; HIERARCHICAL TUCKER; OUTER PRODUCT; STORAGE COMPLEXITY; TENSOR APPROXIMATION; TENSOR RANKS;

EID: 84869490650     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.08.010     Document Type: Article
Times cited : (100)

References (14)
  • 1
    • 77952289640 scopus 로고    scopus 로고
    • A new scheme for the tensor representation
    • W. Hackbusch, and S. Kühn A new scheme for the tensor representation J. Fourier Anal. Appl. 15 2009 706 722
    • (2009) J. Fourier Anal. Appl. , vol.15 , pp. 706-722
    • Hackbusch, W.1    Kühn, S.2
  • 2
    • 77956032667 scopus 로고    scopus 로고
    • Hierarchical singular value decomposition of tensors
    • L. Grasedyck Hierarchical singular value decomposition of tensors SIAM J. Matrix Anal. Appl. 31 2010 2029 2054
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 2029-2054
    • Grasedyck, L.1
  • 3
    • 70449525345 scopus 로고    scopus 로고
    • TT-cross approximation for multidimensional arrays
    • I. Oseledets, and E. Tyrtyshnikov TT-cross approximation for multidimensional arrays Linear Algebra Appl. 432 2010 70 88
    • (2010) Linear Algebra Appl. , vol.432 , pp. 70-88
    • Oseledets, I.1    Tyrtyshnikov, E.2
  • 4
    • 70449528138 scopus 로고    scopus 로고
    • Breaking the curse of dimensionality or how to use SVD in many dimensions
    • I. Oseledets, and E. Tyrtyshnikov Breaking the curse of dimensionality or how to use SVD in many dimensions SIAM J. Sci. Comput. 31 5 2009 3744 3759
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.5 , pp. 3744-3759
    • Oseledets, I.1    Tyrtyshnikov, E.2
  • 7
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • L.R. Tucker Some mathematical notes on three-mode factor analysis Psychometrika 31 1966 279 311
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 9
    • 84870651053 scopus 로고    scopus 로고
    • An introduction to hierarchical rank and TT rank of tensors with examples
    • in preparation. Available from:
    • L. Grasedyck, W. Hackbusch, An introduction to hierarchical rank and TT rank of tensors with examples, CMAM, in preparation. Available from: < http://www.dfg-spp1324.de >.
    • CMAM
    • Grasedyck, L.1    Hackbusch, W.2
  • 10
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T.G. Kolda, and B.W. Bader Tensor decompositions and applications SIAM Rev. 51 3 2009 455 500
    • (2009) SIAM Rev. , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 12
    • 5844381624 scopus 로고    scopus 로고
    • Approximation of boundary element matrices
    • M. Bebendorf Approximation of boundary element matrices Numer. Math. 86 4 2000 565 589
    • (2000) Numer. Math. , vol.86 , Issue.4 , pp. 565-589
    • Bebendorf, M.1
  • 13
    • 70449522299 scopus 로고    scopus 로고
    • Black box low tensor rank approximation using fibre-crosses
    • M. Espig, L. Grasedyck, and W. Hackbusch Black box low tensor rank approximation using fibre-crosses Constr. Approx. 30 2009 557 597
    • (2009) Constr. Approx. , vol.30 , pp. 557-597
    • Espig, M.1    Grasedyck, L.2    Hackbusch, W.3
  • 14
    • 24044501239 scopus 로고    scopus 로고
    • Hybrid cross approximation of integral operators
    • DOI 10.1007/s00211-005-0618-1
    • S. Börm, and L. Grasedyck Hybrid cross approximation of integral operators Numer. Math. 101 2005 221 249 (Pubitemid 41213100)
    • (2005) Numerische Mathematik , vol.101 , Issue.2 , pp. 221-249
    • Borm, S.1    Grasedyck, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.