Structure-preserving low multilinear rank approximation of antisymmetric tensors
For researchers working with antisymmetric tensors (e.g., in quantum chemistry or physics), this provides a theoretically grounded and practical approach to structure-preserving low-rank approximation.
This paper develops methods for low multilinear rank approximation of antisymmetric tensors while preserving antisymmetry, showing that a rank equal to the tensor order reduces to an unstructured rank-1 approximation solvable by the higher-order power method with effective initialization.
This paper 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. 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 algorithm. Particular attention is paid to the important 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.