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Volumn 30, Issue 3, 2009, Pages 557-597

Black box low tensor-rank approximation using fiber-crosses

Author keywords

Black box; Cross approximation; Fiber crosses; Low rank; Newton; Tensor

Indexed keywords


EID: 70449522299     PISSN: 01764276     EISSN: 14320940     Source Type: Journal    
DOI: 10.1007/s00365-009-9076-9     Document Type: Article
Times cited : (38)

References (17)
  • 1
    • 27844496824 scopus 로고    scopus 로고
    • Algorithms for numerical analysis in high dimensions
    • Beylkin, G., Mohlenkamp, M. J.: Algorithms for numerical analysis in high dimensions. SIAM J. Sci. Comput. 26(6), 2133-2159 (2005).
    • (2005) SIAM J. Sci. Comput. , vol.26 , Issue.6 , pp. 2133-2159
    • Beylkin, G.1    Mohlenkamp, M.J.2
  • 2
    • 67349235740 scopus 로고    scopus 로고
    • Multivariate regression and machine learning with sums of separable functions
    • Beylkin, G., Garcke, J., Mohlenkamp, M.: Multivariate regression and machine learning with sums of separable functions. SIAM J. Sci. Comput. 31, 1840-1857 (2009).
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 1840-1857
    • Beylkin, G.1    Garcke, J.2    Mohlenkamp, M.3
  • 3
    • 24044501239 scopus 로고    scopus 로고
    • Hybrid cross approximation of integral operators
    • Börm, S., Grasedyck, L.: Hybrid cross approximation of integral operators. Numer. Math. 101, 221-249 (2005).
    • (2005) Numer. Math. , vol.101 , pp. 221-249
    • Börm, S.1    Grasedyck, L.2
  • 6
    • 41549148748 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • Stanford University
    • de Silva, V., Lim, L.-H.: Tensor rank and the ill-posedness of the best low-rank approximation problem. Technical Report SCCM-06-06, Stanford University (2006).
    • (2006) Technical Report SCCM-06-06
    • de Silva, V.1    Lim, L.-H.2
  • 7
    • 70449518780 scopus 로고    scopus 로고
    • Effiziente Bestapproximation mittels Summen von Elementartensoren in hohen Dimensionen
    • Universität Leipzig
    • Espig, M.: Effiziente Bestapproximation mittels Summen von Elementartensoren in hohen Dimensionen. PhD thesis, Universität Leipzig (2008).
    • (2008) PhD Thesis
    • Espig, M.1
  • 9
    • 3042756404 scopus 로고    scopus 로고
    • Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
    • Grasedyck, L.: Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure. Computing 72, 247-265 (2004).
    • (2004) Computing , vol.72 , pp. 247-265
    • Grasedyck, L.1
  • 11
    • 0036055687 scopus 로고    scopus 로고
    • Orthogonal tensor decompositions
    • Kolda, T. G.: Orthogonal tensor decompositions. SIAM J. Matrix Anal. Appl. 23(1), 243-255 (2001).
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , Issue.1 , pp. 243-255
    • Kolda, T.G.1
  • 12
    • 33750308016 scopus 로고    scopus 로고
    • Minimization methods for approximating tensors and their comparison
    • Oseledets, I. V., Savost'yanov, D. V.: Minimization methods for approximating tensors and their comparison. Comput. Math. Math. Phys. 46(10), 1641-1650 (2006).
    • (2006) Comput. Math. Math. Phys. , vol.46 , Issue.10 , pp. 1641-1650
    • Oseledets, I.V.1    Savost'yanov, D.V.2
  • 14
    • 0030775193 scopus 로고    scopus 로고
    • A weighted non-negative least squares algorithm for three-way 'PARAFAC' factor analysis
    • Paatero, P.: A weighted non-negative least squares algorithm for three-way 'PARAFAC' factor analysis. Chemometrics Intel. Lab. Syst. 38, 223-242 (1997).
    • (1997) Chemometrics Intel. Lab. Syst. , vol.38 , pp. 223-242
    • Paatero, P.1
  • 15
    • 0000020580 scopus 로고
    • Kruskal's polynomial for 2×2×2 arrays and a generalization to 2×n×n
    • Ten Berge, J. M. F.: Kruskal's polynomial for 2×2×2 arrays and a generalization to 2×n×n. Psychometrika 56, 631-636 (1991).
    • (1991) Psychometrika , vol.56 , pp. 631-636
    • Ten, B.J.M.F.1
  • 16
    • 34250386292 scopus 로고
    • Additive structure in qualitative data: An alternating least squares method with optimal scaling features
    • Young, F. W., de Leeuw, J., Takane, Y.: Additive structure in qualitative data: an alternating least squares method with optimal scaling features. Psychometrika 41, 471-503 (1976).
    • (1976) Psychometrika , vol.41 , pp. 471-503
    • Young, F.W.1    de Leeuw, J.2    Takane, Y.3
  • 17
    • 0036056838 scopus 로고    scopus 로고
    • Rank-one approximation to high order tensors
    • Zhang, T., Golub, G. H.: Rank-one approximation to high order tensors. SIAM J. Matrix Anal. Appl. 23(2), 534-550 (2001).
    • (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.