Fast truncation of mode ranks for bilinear tensor operations

By Dmitry V. Savostyanov, E. E. Tyrtyshnikov, Nickolai L. Zamarashkin. 2010

10 citations recorded by the source corpus.

We propose a fast algorithm for mode rank truncation of the result of a bilinear operation on 3‐tensors given in the Tucker or canonical form. If the arguments and the result have mode sizes n and mode ranks r, the computation costs (nr3 + r4). The algorithm is based on the cross approximation of Gram matrices, and the accuracy of the resulted Tucker approximation is limited by square root of the machine precision. We apply the proposed algorithms for the evaluation of the Hadamard square of the electron density and demonstrate that it outperforms previously used methods for this purpose. We also check the accuracy of the resulted Tucker approximation and show that one iteration of the Tucker‐ALS method improves it almost up to the machine precision. Copyright © 2011 John Wiley & Sons, Ltd.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Computational Theory and Mathematics

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

  1. Boris N. Khoromskij
  2. Dmitry V. Savostyanov
  3. Sergey V. Dolgov
  4. Ivan V. Oseledets
  5. E. E. Tyrtyshnikov
  6. Venera Khoromskaia
  7. Wolfgang Hackbusch
  8. Heinz-Jürgen Flad

In Computational Mathematics

  1. Sergey V. Dolgov
  2. Dmitry V. Savostyanov
  3. Boris N. Khoromskij
  4. Ivan V. Oseledets
  5. Vladimir A. Kazeev
  6. Venera Khoromskaia
  7. E. E. Tyrtyshnikov
  8. V. Dolgov

In Computational Theory and Mathematics

  1. Sergey V. Dolgov
  2. Dmitry V. Savostyanov
  3. Boris N. Khoromskij
  4. Ivan V. Oseledets
  5. Venera Khoromskaia
  6. E. E. Tyrtyshnikov
  7. Christine Tobler
  8. V. Dolgov

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