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Computing and Visualization in Science

, Volume 15, Issue 6, pp 331–344 | Cite as

A note on tensor chain approximation

  • Mike Espig
  • Kishore Kumar Naraparaju
  • Jan SchneiderEmail author
Article

Abstract

This paper deals with the approximation of \(d\)-dimensional tensors, as discrete representations of arbitrary functions \(f(x_1,\ldots ,x_d)\) on \([0,1]^d\), in the so-called tensor chain format. The main goal of this paper is to show that the construction of a tensor chain approximation is possible using skeleton/cross approximation type methods. The complete algorithm is described, computational issues are discussed in detail and the complexity of the algorithm is shown to be linear in \(d\). Some numerical examples are given to validate the theoretical results.

Keywords

Cross approximation Skeleton decomposition Tensor chain format Singular value decomposition 

Mathematical Subject Classification

15A69 41A63 65F30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mike Espig
    • 1
  • Kishore Kumar Naraparaju
    • 2
  • Jan Schneider
    • 3
    Email author
  1. 1.RWTH Aachen UniversityAachenGermany
  2. 2.BITS-Pilani Hyderabad CampusHyderabadIndia
  3. 3.University of RostockRostockGermany

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