CP DECOMPOSITION AND LOW-RANK APPROXIMATION OF ANTISYMMETRIC TENSORS

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.