Approximation rates for the hierarchical tensor format in periodic Sobolev spaces |
| |
Authors: | Reinhold Schneider André Uschmajew |
| |
Institution: | 1. Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany;2. MATHICSE-ANCHP, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland |
| |
Abstract: | In this note we estimate the asymptotic rates for the L2-error decay and the storage cost when approximating 2π-periodic, d-variate functions from isotropic and mixed Sobolev classes by the recent hierarchical tensor format as introduced by Hackbusch and Kühn. 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. |
| |
Keywords: | Approximation of multi-variate functions Hierarchical tensor format Hierarchical Tucker rank High-order SVD Bilinear approximation |
本文献已被 ScienceDirect 等数据库收录! |