Structure-preserving low multilinear rank approximation of antisymmetric tensors

Applied and Computational Mathematics Seminar
Monday, November 18, 2019 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Erna Begovic Kovac – GT Math
Luca Dieci

The talk is concerned with low multilinear rank approximations to antisymmetric tensors, that is, multivariate arrays for which the entries change sign when permuting pairs of indices. Such tensors play a major role in quantum chemistry. We show which ranks can be attained by an antisymmetric tensor and discuss the adaption of existing approximation algorithms to preserve antisymmetry, most notably a Jacobi-type algorithm. Particular attention is paid to the special case when choosing the rank equal to the order of the tensor. It is shown that this case can be addressed with an unstructured rank-1 approximation. This allows for the straightforward application of the higher-order power method, for which we discuss effective initialization strategies. This is a joint work with Daniel Kressner (EPFL).