In tensor theory, the parallel factorization(PARAFAC)decomposition expresses a tensor as the sum of a set of rank-1 tensors. By carrying out this numerical decomposition, mixed sources can be separated or unknown system parameters can be identified, which is the so-called blind source separation or blind identification. In this paper we propose a numerical PARAFAC decomposition algorithm. Compared to traditional algorithms, we speed up the decomposition in several aspects, i.e., search direction by extrapolation, suboptimal step size by Gauss-Newton approximation, and linear search by n steps. The algorithm is applied to polarization sensitive array parameter estimation to show its usefulness. Simulations verify the correctness and performance of the proposed numerical techniques.
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