Constructive Approximation

, Volume 34, Issue 3, pp 371–391

Regularity of Tensor Product Approximations to Square Integrable Functions


DOI: 10.1007/s00365-010-9125-4

Cite this article as:
Uschmajew, A. Constr Approx (2011) 34: 371. doi:10.1007/s00365-010-9125-4


We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to square integrable functions. They reveal that the best approximation and all of its factors have the same smoothness as the approximated function itself. This is not obvious, since the approximation is performed in L2.


Tensor productsLow-rank approximationOptimal subspace approximationSobolev spaces

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany