메뉴 건너뛰기




Volumn 438, Issue 2, 2013, Pages 891-918

Krylov-type methods for tensor computations i

Author keywords

Information science; Krylov type method; Multilinear algebra; Multilinear rank; Sparse tensor; Tensor; Tensor approximation; Tucker model

Indexed keywords

HIGHER ORDER SINGULAR VALUE DECOMPOSITION; KRYLOV METHOD; KRYLOV-TYPE METHOD; MULTILINEAR ALGEBRA; MULTILINEAR RANK; NUMERICAL EXPERIMENTS; RECURSIONS; STRUCTURED TENSORS; SYNTHETIC DATASETS; TENSOR APPROXIMATION; TENSOR PRODUCTS;

EID: 84869495056     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.12.007     Document Type: Article
Times cited : (30)

References (33)
  • 1
    • 0032563594 scopus 로고    scopus 로고
    • Improving the speed of multi-way algorithms: Part I. Tucker3
    • DOI 10.1016/S0169-7439(98)00010-0, PII S0169743998000100
    • C. Andersson, and R. Bro Improving the speed of multi-way algorithms: part I. Tucker 3 Chemomet. Intell. Lab. Syst. 42 1998 93 103 (Pubitemid 28440364)
    • (1998) Chemometrics and Intelligent Laboratory Systems , vol.42 , Issue.1-2 , pp. 93-103
    • Andersson, C.A.1    Bro, R.2
  • 2
    • 33845525246 scopus 로고    scopus 로고
    • Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
    • DOI 10.1145/1186785.1186794
    • B.W. Bader, and T.G. Kolda Algorithm 862: MATLAB tensor classes for fast algorithm prototyping ACM Trans. Math. Softw. 32 4 2006 635 653 (Pubitemid 44927149)
    • (2006) ACM Transactions on Mathematical Software , vol.32 , Issue.4 , pp. 635-653
    • Bader, B.W.1    Kolda, T.G.2
  • 3
    • 49749096526 scopus 로고    scopus 로고
    • Efficient MATLAB computations with sparse and factored tensors
    • URL
    • B.W. Bader, and T.G. Kolda Efficient MATLAB computations with sparse and factored tensors SIAM J. Sci. Comput. 30 1 2007 205 231 URL:
    • (2007) SIAM J. Sci. Comput. , vol.30 , Issue.1 , pp. 205-231
    • Bader, B.W.1    Kolda, T.G.2
  • 4
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition
    • J.D. Carroll, and J.J. Chang Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition Psychometrika 35 1970 283 319
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.D.1    Chang, J.J.2
  • 5
    • 0346238834 scopus 로고    scopus 로고
    • Tensor decompositions
    • J.G. McWhirter, I.K. Proudler, Clarendon Press Oxford, UK
    • P. Comon Tensor decompositions J.G. McWhirter, I.K. Proudler, Mathematics in Signal Processing V 2002 Clarendon Press Oxford, UK 1 24
    • (2002) Mathematics in Signal Processing v , pp. 1-24
    • Comon, P.1
  • 8
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • URL
    • V. de Silva, and L.H. Lim Tensor rank and the ill-posedness of the best low-rank approximation problem SIAM J. Matrix Anal. Appl. 30 3 2008 1084 1127 URL:
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , Issue.3 , pp. 1084-1127
    • De Silva, V.1    Lim, L.H.2
  • 11
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • G.H. Golub, and W. Kahan Calculating the singular values and pseudo-inverse of a matrix SIAM J. Numer. Anal. Ser. B 2 1965 205 224
    • (1965) SIAM J. Numer. Anal. Ser. B , vol.2 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 12
    • 84869505598 scopus 로고    scopus 로고
    • Wedderburn rank reduction and Krylov subspace method for tensor approximation, Part 1: Tucker case
    • Russian Academy of Sciences
    • S. Goreinov, I. Oseledets, D. Savostyanov, Wedderburn rank reduction and Krylov subspace method for tensor approximation, Part 1: Tucker case, Tech. Rep. Preprint 2010-01, Inst. Numer. Math., Russian Academy of Sciences, 2010.
    • (2010) Tech. Rep. Preprint 2010-01, Inst. Numer. Math.
    • Goreinov, S.1    Oseledets, I.2    Savostyanov, D.3
  • 13
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis
    • R.A. Harshman Foundations of the PARAFAC procedure: models and conditions for an explanatory multi-modal factor analysis UCLA Working Papers Phonet. 16 1970 1 84
    • (1970) UCLA Working Papers Phonet. , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 14
    • 85163188929 scopus 로고
    • Multiple invariants and generalized rank of a p-way matrix or tensor
    • F.L. Hitchcock Multiple invariants and generalized rank of a p-way matrix or tensor J. Math. Phys. Camb. 7 1927 39 70
    • (1927) J. Math. Phys. Camb. , vol.7 , pp. 39-70
    • Hitchcock, F.L.1
  • 16
    • 2542575037 scopus 로고    scopus 로고
    • Taking a new look at the latent semantic analysis approach to information retrieval
    • M.W. Berry, SIAM Philadelphia, PA
    • E.R. Jessup, and J.H. Martin Taking a new look at the latent semantic analysis approach to information retrieval M.W. Berry, Computational Information Retrieval 2001 SIAM Philadelphia, PA 121 144
    • (2001) Computational Information Retrieval , pp. 121-144
    • Jessup, E.R.1    Martin, J.H.2
  • 17
    • 84897586218 scopus 로고    scopus 로고
    • Multigrid accelerated tensor approximation of function related multidimensional arrays
    • URL
    • B.N. Khoromskij, and V. Khoromskaia Multigrid accelerated tensor approximation of function related multidimensional arrays SIAM J. Sci. Comput. 31 4 2009 3002 3026 URL:
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.4 , pp. 3002-3026
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 20
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • URL
    • T.G. Kolda, and B.W. Bader Tensor decompositions and applications SIAM Rev. 51 3 2009 455 500 URL:
    • (2009) SIAM Rev. , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 21
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least squares algorithms
    • P.M. Kroonenbeg Principal component analysis of three-mode data by means of alternating least squares algorithms Psychometrika 45 1980 69 97
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenbeg, P.M.1
  • 24
    • 84869133470 scopus 로고    scopus 로고
    • A $1 million research bargain for netflix, and maybe a model for others
    • September 21
    • S. Lohr, A $1 million research bargain for netflix, and maybe a model for others, The New York Times, September 21, 2009. URL: .
    • (2009) The New York Times
    • Lohr, S.1
  • 25
    • 51849118006 scopus 로고    scopus 로고
    • Tucker dimensionality reduction of three-dimensional arrays in linear time
    • URL
    • I.V. Oseledets, D.V. Savostianov, and E.E. Tyrtyshnikov Tucker dimensionality reduction of three-dimensional arrays in linear time SIAM J. Matrix Anal. Appl. 30 3 2008 939 956 URL:
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , Issue.3 , pp. 939-956
    • Oseledets, I.V.1    Savostianov, D.V.2    Tyrtyshnikov, E.E.3
  • 27
    • 33750527967 scopus 로고    scopus 로고
    • Handwritten digit classification using higher order singular value decomposition
    • DOI 10.1016/j.patcog.2006.08.004, PII S0031320306003542
    • B. Savas, and L. Eldén Handwritten digit classification using higher order singular value decomposition Pattern Recognit. 40 2007 993 1003 (Pubitemid 44667764)
    • (2007) Pattern Recognition , vol.40 , Issue.3 , pp. 993-1003
    • Savas, B.1    Elden, L.2
  • 28
    • 79251508042 scopus 로고    scopus 로고
    • Quasi-Newton methods on Grassmannians and multilinear approximations of tensors
    • URL
    • B. Savas, and L.H. Lim Quasi-Newton methods on Grassmannians and multilinear approximations of tensors SIAM J. Sci. Comput. 32 6 2010 3352 3393 URL:
    • (2010) SIAM J. Sci. Comput. , vol.32 , Issue.6 , pp. 3352-3393
    • Savas, B.1    Lim, L.H.2
  • 30
    • 0036018626 scopus 로고    scopus 로고
    • A Krylov-Schur algorithm for large eigenproblems
    • URL
    • G.W. Stewart A Krylov-Schur algorithm for large eigenproblems SIAM J. Matrix Anal. Appl. 23 3 2002 601 614 URL:
    • (2002) SIAM J. Matrix Anal. Appl. , vol.23 , Issue.3 , pp. 601-614
    • Stewart, G.W.1
  • 32
    • 0000666371 scopus 로고
    • The extension of factor analysis to three-dimensional matrices
    • L.R. Tucker The extension of factor analysis to three-dimensional matrices Contrib. Math. Psych. 1964 109 127
    • (1964) Contrib. Math. Psych. , pp. 109-127
    • Tucker, L.R.1
  • 33
    • 0036056838 scopus 로고    scopus 로고
    • Rank-one approximation to high order tensors
    • URL
    • T. Zhang, and G.H. Golub Rank-one approximation to high order tensors SIAM J. Matrix Anal. Appl. 23 2 2001 534 550 URL:
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , Issue.2 , pp. 534-550
    • Zhang, T.1    Golub, G.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.