Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method

The Candecomp/Parafac decomposition (CPD) of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which computing the CPD is equivalent to solving a structured polynomial system that is determined by the full rank factorization of the matricization of the tensor. Under the generic uniqueness conditions, the CPD solutions of the system are isolated so that these solutions can be achieved by homotopy method.