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We study the least-squares functional of the canonical polyadic decomposition by elimination of one factor matrix,which leads to a reduced functional.An analysis of the reduced functional gives several equivalent optimization problems,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 two fixed point iterations for approximating the best rank-one and the best rank-R decomposition under certain non-degeneracy conditions.