Fall 2014

A Few Computational Tools for Tensor Rank and Tensor Decomposition

Monday, November 17th, 2014 1:30 pm2:30 pm

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We begin by reviewing some useful M2 commands to work with tensors, starting from Sylvester algorithm to write a binary form as a sum of powers. We discuss two algorithms to check the identifiability of a specific tensor. The first one is deterministic (joint with Chiantini and Vannieuwenhoven) and explores the geometry of the decomposition, by computing the tangent space of the contact variety. The second one is probabilistic and uses software Bertini and homotopic continuation methods (joint with Hauenstein, Oeding, Sommese).