Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

@article{Oseledets2009BreakingTC,
  title={Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions},
  author={Ivan V. Oseledets and Eugene E. Tyrtyshnikov},
  journal={SIAM J. Scientific Computing},
  year={2009},
  volume={31},
  pages={3744-3759}
}

• Ivan V. Oseledets, Eugene E. Tyrtyshnikov
• Published in SIAM J. Scientific Computing 2009
• DOI:10.1137/090748330

For d-dimensional tensors with possibly large d > 3, an hierarchical data structure, called the Tree-Tucker format, is presented as an alternative to the canonical decomposition. It has asymptotically the same (and often even smaller) number of representation parameters and viable stability properties. The approach involves a recursive construction described by a tree with the leafs corresponding to the Tucker decompositions of three-dimensional tensors, and is based on a sequence of SVDs for… CONTINUE READING

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