id: 06008918
dt: j
an: 06008918
au: Oseledets, I.V.
ti: Tensor-train decomposition.
so: SIAM J. Sci. Comput. 33, No. 5, 2295-2317 (2011).
py: 2011
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: tensors; high-dimensional problems; SVD; TT-format
ci: 
li: doi:10.1137/090752286
ab: 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.
rv: