SEMINARIO DEL DOTTORATO
LUNEDI' 20 MAGGIO 2013 ALLE ORE 14,30 presso la Sala Conferenze "F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI" Il Prof. Nick Vannieuwenhoven ( Leuven University ) terrà una conferenza dal titolo: "On generalizing the Schmidt-Eckart-Young theorem to tensors" Abstract: The Schmidt--Eckart--Young theorem for matrices (order two tensors) states that the optimal rank-r approximation to a matrix is obtained by retaining the first r terms of the singular value decomposition, which always exists. In this talk, we consider a generalization of this optimal truncation property for the CANDECOMP/PARAFAC decomposition for tensors of higher order. A necessary orthogonality condition is presented, and, using a dimensionality argument involving the underlying algebraic varieties, it is shown that the Schmidt--Eckart--Young theorem cannot be extended to generic tensors of small rank. We also investigate a probabilistic numerical algorithm to compute the dimension of the aforementioned algebraic variety, revealing a general algorithm to test with high probability the singularity of any structured matrix admitting an efficient matrix-vector product implementation, using only inexact arithmetic