Tensor-Train Decomposition

@article{Oseledets2011TensorTrainD,
  title={Tensor-Train Decomposition},
  author={I. Oseledets},
  journal={SIAM J. Sci. Comput.},
  year={2011},
  volume={33},
  pages={2295-2317}
}
  • I. Oseledets
  • Published 2011
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 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… CONTINUE READING
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