Constructive Approximation

, Volume 37, Issue 1, pp 1–18 | Cite as

Constructive Representation of Functions in Low-Rank Tensor Formats

  • I. V. OseledetsEmail author


In this paper, we obtain explicit representations of several multivariate functions in the Tensor Train (TT) format and explicit TT-representations of tensors that stem from the tensorization of univariate functions on grids. Previous results contained only estimates on the number of parameters (tensor ranks), and this paper fills this gap by providing explicit low-parametric representations for these functions and tensors.


TT-format QTT-format Tensor decompositions Multivariate functions Explicit representations 

Mathematics Subject Classification

15A69 41A30 



I am thankful to the anonymous referees. Their comments helped to improve the paper a lot.

Supported by RFBR grants, 12-01-00546-a, 12-01-33013-mol-a-ved, 11-01-12137-ofi-m-2011, 11-01-00549-a, by Rus. Gov. Contracts Π1112, 14.740.11.0345, 14.740.11.1067, 16.740.12.0727 by Rus. President grant MK-140.2011.1, by Priority Research Program OMN-3, by Dmitriy Zimin Dynasty Foundation. Part of this work was done during the stay of the author in Max-Planck Institute for Mathematics in Sciences, Leipzig.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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