Volume 62, pp. 72-94, 2024.

CP decomposition and low-rank approximation of antisymmetric tensors

Erna Begović Kovač and Lana Periša

Abstract

For antisymmetric tensors, the paper examines a low-rank approximation that 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 an 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 the Julia programming language and their numerical performance is discussed.

Full Text (PDF) [377 KB], BibTeX , DOI: 10.1553/etna_vol62s72

Key words

CP decomposition, antisymmetric tensors, low-rank approximation, structure-preserving algorithm, Julia

AMS subject classifications

15A69