  In this paper, we present a method to certify the approximation quality of a
low rank tensor to a given third order symmetric tensor. Under mild
assumptions, best low rank approximation is attained if a control parameter is
zero or quantified quasi-optimal low rank approximation is obtained if the
control parameter is positive.This is based on a primal-dual method for
computing a low rank approximation for a given tensor. The certification is
derived from the global optimality of the primal and dual problems, and is
characterized by easily checkable relations between the primal and the dual
solutions together with another rank condition. The theory is verified
theoretically for orthogonally decomposable tensors as well as numerically
through examples in the general case.
