presso la Sala Conferenze "F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il dott. Nick Vannieuwenhoven
(KU Leuven)
terrà una conferenza dal titolo:
"Hitchcock's rank decomposition: an algebraic geometry point of view"
Abstract:
Hitchcock's rank decomposition--also known as Candecomp or Parafac--can be considered a generalization of a low-rank decomposition of a matrix, that is, an element of a tensor product space with two factors, to the setting of tensor product spaces with more factors. This generalization admits several peculiar properties that are not yet fully understood. In this talk, we will investigate two of its properties using techniques from algebraic geometry. In the first part, we show that a classic technique for computing a low-rank matrix decomposition, namely successively computing rank-1 approximations, does not generalize to the tensor setting: such an approximation scheme will not recover the rank decomposition. In the second part of the talk, we investigate the generic uniqueness of a rank decomposition. An algorithm is presented for proving this property for tensors of sufficiently small rank. We show that generic uniqueness holds in every tensor product space of dimension less than 15,000 for every rank up to the generic rank of the space minus one.
This work was performed in collaboration with L. Chiantini (Universita' di Siena), J. Nicaise (KU Leuven), and G. Ottaviani (Universita' di Firenze).