메뉴 건너뛰기




Volumn 33, Issue 3, 2011, Pages 1315-1328

Algebraic wavelet transform via quantics tensor train decomposition

Author keywords

Discrete wavelet transform; Quantics tensor train format; Tensor train format

Indexed keywords

ORTHOGONAL FUNCTIONS; SIGNAL RECONSTRUCTION; TENSORS; WAVELET DECOMPOSITION;

EID: 79960391206     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100811647     Document Type: Article
Times cited : (22)

References (16)
  • 1
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms. I
    • G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms. I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 3
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • 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 (2008), pp. 1084-1127.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 1084-1127
    • De Silva, V.1    Lim, L.-H.2
  • 4
    • 79960403660 scopus 로고    scopus 로고
    • Polynomial approximation in hierarchical Tucker format by vectortensorization
    • submitted
    • L. Grasedyck, Polynomial approximation in hierarchical Tucker format by vectortensorization, BIT, submitted.
    • BIT
    • Grasedyck, L.1
  • 5
    • 79960994573 scopus 로고    scopus 로고
    • O(d logN)-quantics approximation of N-d tensors in high-dimensional numerical modeling
    • to appear
    • B. N. Khoromskij, O(d logN)-quantics approximation of N-d tensors in high-dimensional numerical modeling, Constr. Approx., to appear.
    • Constr. Approx.
    • Khoromskij, B.N.1
  • 7
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev., 51 (2009), pp. 455-500.
    • (2009) SIAM Rev. , vol.51 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 8
    • 69549090266 scopus 로고    scopus 로고
    • A new tensor decomposition
    • I. V. Oseledets, A new tensor decomposition, Dokl. Math., 80 (2009), pp. 495-496.
    • (2009) Dokl. Math. , vol.80 , pp. 495-496
    • Oseledets, I.V.1
  • 9
    • 70350271433 scopus 로고    scopus 로고
    • Approximation of matrices with logarithmic number of parameters
    • I. V. Oseledets, Approximation of matrices with logarithmic number of parameters, Dokl. Math., 80 (2009), pp. 653-654.
    • (2009) Dokl. Math. , vol.80 , pp. 653-654
    • Oseledets, I.V.1
  • 11
    • 77956042755 scopus 로고    scopus 로고
    • Approximation of 2d × 2d matrices using tensor decomposition
    • I. V. Oseledets, Approximation of 2d × 2d matrices using tensor decomposition, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2130-2145.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 2130-2145
    • Oseledets, I.V.1
  • 12
    • 70449528138 scopus 로고    scopus 로고
    • Breaking the curse of dimensionality, or how to use SVD in many dimensions
    • I. V. Oseledets and E. E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions, SIAM J. Sci. Comput., 31 (2009), pp. 3744-3759.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 3744-3759
    • Oseledets, I.V.1    Tyrtyshnikov, E.E.2
  • 14
    • 70449525345 scopus 로고    scopus 로고
    • TT-cross approximation for multidimensional arrays
    • I. V. Oseledets and E. E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra Appl., 432 (2010), pp. 70-88.
    • (2010) Linear Algebra Appl. , vol.432 , pp. 70-88
    • Oseledets, I.V.1    Tyrtyshnikov, E.E.2
  • 16
    • 0142055272 scopus 로고    scopus 로고
    • Tensor approximations of matrices generated by asymptotically smooth functions
    • E. E. Tyrtyshnikov, Tensor approximations of matrices generated by asymptotically smooth functions, Sb. Math., 194 (2003), pp. 941-954. (Pubitemid 37282737)
    • (2003) Sbornik Mathematics , vol.194 , Issue.5-6 , pp. 941-954
    • Tyrtyshnikov, E.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.