Computation of extreme eigenvalues in higher dimensions using block tensor train format

@article{Dolgov2014ComputationOE,
  title={Computation of extreme eigenvalues in higher dimensions using block tensor train format},
  author={S. V. Dolgov and Boris N. Khoromskij and Ivan V. Oseledets and Dmitry V. Savostyanov},
  journal={Computer Physics Communications},
  year={2014},
  volume={185},
  pages={1207-1216}
}
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high–dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. Applying a block version of the TT format to several vectors simultaneously, we compute the low–lying eigenstates of a system byminimization of a block Rayleigh quotient performed in an alternating fashion… CONTINUE READING

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