Approximation rates for the hierarchical tensor format in periodic Sobolev spaces

In this note we estimate the asymptotic rates for the L-2-error decay and the storage cost when approximating 2 pi-periodic, d-variate functions from isotropic and mixed Sobolev classes by the recent hierarchical tensor format as introduced by Hackbusch and Kuhn. To this end, we survey some results on bilinear approximation due to Temlyakov. The approach taken in this paper improves and generalizes recent results of Griebel and Harbrecht for the bi-variate case. (C) 2013 Elsevier Inc. All rights reserved.


Published in:
Journal of Complexity, 30, 2, 56-71
Year:
2014
Publisher:
San Diego, Academic Press Inc Elsevier Science
ISSN:
0885-064X
Keywords:
Laboratories:




 Record created 2014-05-02, last modified 2018-09-13


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