Generic Properties of Symmetric Tensors
In: TRICAP2006, 4-9 June 2006, Crete, Greece.
Little has been published about rank-revealing decompositions of symmetric tensors. Definitions of rank are discussed, and useful results on Generic Rank are proved, with the help of tools borrowed from Algebraic Geometry.
For instance for several years, the so-called ALS algorithm is used
to fit data arrays to the Parafac multilinear model. Yet, the minimization of this matching error is an ill-posed problem in general, since the set of tensors of rank smaller than r is not closed, unless r=1.