Tensorisation of vectors and their efficient convolution

Numerische Mathematik

Volumn 119, Issue 3, 2011, Pages 465-488

  Hackbusch, Wolfgang ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

15A69; 15A99; 44A35; 65F99; 65T99

Indexed keywords

EID: 80053999286     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-011-0393-0     Document Type: Article

References (9)

1. Braess D., Hackbusch W.: On the efficient computation of high-dimensional integrals and the approximation by exponential sums. In: DeVore, R., Kunoth, A. (eds) Multiscale, nonlinear and adaptive approximation, pp. 39-74. Springer, Berlin (2009).
2. Espig, M.: Effiziente Bestapproximation mittels Summen von Elementartensoren in hohen Dimensionen. Doctoral thesis, University Leipzig (2008).
3. Grasedyck, L.: Polynomial approximation in hierarchical Tucker format by vector-tensorization. Submitted (2010).
4. Hackbusch W.: Convolution of hp-functions on locally refined grids. IMA J. Numer. Anal. 29, 960-985 (2009).
5. Hackbusch, W.: Tensor spaces and numerical tensor calculus. Monograph (in preparation).
6. Hackbusch W., Kühn S.: A new scheme for the tensor representation. J. Fourier Anal. Appl. 15, 706-722 (2009).
7. Khoromskij, B. N.: O(d log N)-quantics approximation of N-d tensors in high-dimensional numerical modeling. Constr. Approx (2011). doi: 10. 1007/s00365-011-9131-1.
8. d matrices using tensor decomposition. SIAM J. Matrix Anal. Appl. 31, 2130-2145 (2010).
9. Oseledets I. V., Tyrtyshnikov E. E.: Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput. 31, 3744-3759 (2009).