Waring decompositions and identifiability via Bertini and Macaulay2 software. (March 2019)

• Record Type: Journal Article
• Authors: Angelini, Elena
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 200
• Page End: 212
• Publication Date: 2019-03
• Subjects: 15A69 -- 14P05 -- 14Q99 -- 13P05 -- 65H10; Waring decomposition -- Complex identifiability -- Real identifiability -- Numerical algebraic geometry -- Hessian criterion; 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.2018.06.021
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Starting from our previous papersAngelini et al. (2018c) andAngelini et al. (2018a), we prove the existence of a non-empty Euclidean open subset whose elements are polynomial vectors with 4 components, in 3 variables, degrees, respectively, 2, 3, 3, 3 and rank 6, which are not identifiable over C but are identifiable over R . This result has been obtained via computer-aided procedures suitably adapted to investigate the number of Waring decompositions for general polynomial vectors over the fields of complex and real numbers. Furthermore, by means of the Hessian criterion (Chiantini et al., 2014 ), we prove identifiability over C for polynomial vectors in many cases of sub-generic rank.