Fast truncation of mode ranks for bilinear tensor operations

@article{Savostyanov2012FastTO,
  title={Fast truncation of mode ranks for bilinear tensor operations},
  author={Dmitry V. Savostyanov and Eugene E. Tyrtyshnikov and Nickolai Zamarashkin},
  journal={Numer. Linear Algebra Appl.},
  year={2012},
  volume={19},
  pages={103-111}
}
SUMMARY 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… Expand
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