New Algorithms for tensor decomposition based on a reduced functional

We study the least-squares functional of the canonical polyadic tensor decomposition for third order tensors by eliminating one factor matrix, which leads to a reduced functional. An analysis of the reduced functional leads to several equivalent optimization problem, like a Rayleigh quotient or a projection. These formulations are the basis of several new algorithms: the Centroid Projection method for efficient computation of suboptimal solutions and fixed-point iteration methods for approximating the best rank-1 and the best rank-R decompositions under certain nondegeneracy conditions.