Tensor-Train Decomposition
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 approxi...
Saved in:
Published in | SIAM journal on scientific computing Vol. 33; no. 5; pp. 2295 - 2317 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2011
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
ISSN: | 1064-8275 1095-7197 |
DOI: | 10.1137/090752286 |