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SIAM J. on Scientific Computing / Volume 33 / Issue 5

SIAM J. Sci. Comput. 33, pp. 2295-2317 (23 pages)

Tensor-Train Decomposition

I. V. Oseledets

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A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices. The new form gives a clear and convenient way to implement all basic operations efficiently. A fast rounding procedure is presented, as well as basic linear algebra operations. Examples showing the benefits of the decomposition are given, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.

© 2011 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

15A23, 15A69, 65F99

PUBLICATION DATA

ISSN

1064-8275 (print)  
1095-7197 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received March 10, 2009
Accepted June 19, 2011
Published online September 22, 2011
Digital Object Identifier
http://dx.doi.org/10.1137/090752286

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