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Structure-preserving low multilinear rank approximation of antisymmetric tensors. (arXiv:1603.05010v2 [math.NA] UPDATED)
来源于:arXiv
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. 查看全文>>