  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.
