  For a given symmetric tensor, we aim at finding a new one whose symmetric
rank is small and that is close to the given one. There exist linear relations
among the entries of low rank symmetric tensors. Such linear relations can be
expressed by polynomials, which are called generating polynomials. We propose a
new approach for computing low rank approximations by using generating
polynomials. First, we estimate a set of generating polynomials that are
approximately satisfied by the given tensor. Second, we find approximate common
zeros of these polynomials. Third, we use these zeros to construct low rank
tensor approximations. If the symmetric tensor to be approximated is
sufficiently close to a low rank one, we show that the computed low rank
approximations are quasi-optimal.
