Effective identifiability criteria for tensors and polynomials. (July 2018)

• Record Type: Journal Article
• Authors: Massarenti, Alex; Mella, Massimiliano; Staglianò, Giovanni
• Is Part Of: Journal of symbolic computation. Volume 87(2018)
• Page Start: 227
• Page End: 237
• Publication Date: 2018-07
• Subjects: Tensor decomposition -- Waring decomposition -- Effective identifiability; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.11.006
• Languages: English
• ISSNs: 0747-7171

Abstract

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.