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arXiv · 2212.13389

CP decomposition and low-rank approximation of antisymmetric tensors

Erna Begovic·Lana Perisa
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Abstract

For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for finding such approximation. Moreover, we show that this approximation problem is equivalent to the problem of finding the best multilinear low-rank antisymmetric approximation and, consequently, equivalent to the problem of finding the best unstructured rank-$1$ approximation. The case of partial antisymmetry is also discussed. The algorithms are implemented in Julia programming language and their numerical performance is discussed.

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Erna Begovic, Lana Perisa. 2022-12-27. CP decomposition and low-rank approximation of antisymmetric tensors. https://doi.org/10.1553/etna_vol62s72

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