Effective identifiability criteria for tensors and polynomials. (July 2018) - Massarenti, Alex; Mella, Massimiliano; Staglianò, Giovanni
Abstract: A tensor T, in a given tensor space, is said to be h -identifiable if it admits a unique decomposition as a sum of h rank one tensors. A criterion for h -identifiability is called effective if it is satisfied in a dense, open subset of the set of rank h tensors. In this paper we give effective h -identifiability criteria for a large class of tensors. We then improve these criteria for some symmetric tensors. For instance, this allows us to give a complete set of effective identifiability criteria for ternary quintic polynomials. Finally, we implement our identifiability algorithms in Macaulay2.