Constructive Representation of Functions in Low-Rank Tensor Formats

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54 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalConstructive Approximation
Volume37
Issue number1
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

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

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