Fast truncation of mode ranks for bilinear tensor operations

Details Fast truncation of mode ranks for bilinear tensor operations Fast truncation of mode ranks for bilinear tensor operations

2010-04-27

arxiv.org/abs/1004.4919v1

Numerical Linear Algebra with Applications, V. 19(1), pp. 103-111, (2012)

Mathematics

Numerical Analysis

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

Scientific paper

10.1002/nla.765

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 $O(nr^3 + r^4)$. 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.

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