engleski

Structure-preserving low multilinear rank approximation of antisymmetric tensors

We are concerned with finding low multilinear approximation B to a given antisymmetric tensor A, such that B is again antisymmetric. We show which multilinear ranks can be attained by an antisymmetric tensor. We discuss the adaption of existing approximation algorithms, most notably a Jacobi-type algorithm. Particular attention is paid to the important special case when choosing the rank equal to the order of the tensor. We show that a best unstructured rank-1 approximation can always be turned into a best antisymmetric multilinear rank-d approximation. This allows the straightforward application of the higher-order power method, for which we consider effective initialization strategies.

tensor; low rank; Jacobi rotation

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