Waring, tangential and cactus decompositions

Abstract

(EN) We revise the famous algorithm for symmetric tensor decomposition due to Brachat, Comon, Mourrain and Tsidgaridas. Afterwards, we generalize it in order to detect possibly different decompositions involving points on the tangential variety of a Veronese variety. Finally, we produce an algorithm for cactus rank and decomposition, which also detects the support of the minimal apolar scheme and its length at each component. (FR) Nous revenons sur le fameux algorithme de Brachat, Comon, Mourrain et Tsidgaridas pour la dćomposition des tenseurs symétriques. Ensuite, nous le généralisons afin de détecter de possibles décompositions différentes impliquant des points sur la variété tangentielle d'une variété de Veronese. Enfin, nous proposons un algorithme pour le rang et la décomposition cactus, qui, lui aussi, détecte le support du schéma apolaire minimal ainsi que sa longueur sur chaque composante.

37 pages

References in corpus (3)

• The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
• Matrix product states and the quantum max-flow/min-cut conjectures
• Algebraic stories from one and from the other pockets

Cited by in corpus (6)

• Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
• On schemes evinced by generalized additive decompositions and their regularity
• A Normal Form Algorithm for Tensor Rank Decomposition
• Minimality and uniqueness for decompositions of specific ternary forms
• Hilbert Functions of Chopped Ideals
• Identifiability and singular locus of secant varieties to spinor varieties