Institute of Mathematics


Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

On nonclosed tensor formats

Talk by Prof. Dr. Wolfgang Hackbusch

Date: 01.12.21  Time: 16.15 - 17.15  Room: Online ZHACM

Since tensor spaces may have a huge dimension, it is often not possible to store tensors by all their entries. Instead one uses certain representations (also called 'formats'), which describe a subset of tensors. For some formats used in practice the set of representable tensors is not closed. This leads to an instability comparable with the cancellation effect in the case of numerical differentiation. Under general conditions we prove for the finite-dimensional case that there is some minimal strength of the instability. For the special case of the 2-term format a quantitative result can be proved. In the infinite-dimensional case with a tensor norm not weaker than the injective crossnorm, the same instability behaviour can be proved. Even the constants in the estimates are under control. As a result, it is sufficient to study the instability behaviour for finite-dimensional model spaces.