English

Fast truncation of mode ranks for bilinear tensor operations

Numerical Analysis 2012-02-07 v1

Abstract

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 O(nr3+r4)O(nr^3 + r^4). 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 machine precision.

Keywords

Cite

@article{arxiv.1004.4919,
  title  = {Fast truncation of mode ranks for bilinear tensor operations},
  author = {Dmitry Savostyanov and Eugene Tyrtyshnikov and Nikolay Zamarashkin},
  journal= {arXiv preprint arXiv:1004.4919},
  year   = {2012}
}

Comments

9 pages, 2 tables. Submitted to Numerical Linear Algebra and Applications, special edition for ICSMT conference, Hong Kong, January 2010