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Jacobi algorithm for the best low multilinear rank approximation of symmetric tensors
 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
, 2013
"... The problem discussed in this paper is the symmetric best low multilinear rank approximation of thirdorder symmetric tensors. We propose an algorithm based on Jacobi rotations, for which symmetry is preserved at each iteration. Two numerical examples are provided indicating the need for such algo ..."
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The problem discussed in this paper is the symmetric best low multilinear rank approximation of thirdorder symmetric tensors. We propose an algorithm based on Jacobi rotations, for which symmetry is preserved at each iteration. Two numerical examples are provided indicating the need for such algorithms. An important part of the paper consists of proving that our algorithm converges to stationary points of the objective function. This can be considered an advantage of the proposed algorithm over existing symmetrypreserving algorithms in the literature.
A prewhiteninginduced bound on the identification error in independent component analysis
 IEEE Trans. Circuits Syst. I, Reg. Papers
, 2005
"... Abstract—In this paper, we derive a prewhiteninginduced lowerbound on the Frobenius norm of the difference between the true mixing matrix and its estimate in independent component analysis. This bound applies to all algorithms that employ a prewhitening. Our analysis allows one to assess the contri ..."
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Abstract—In this paper, we derive a prewhiteninginduced lowerbound on the Frobenius norm of the difference between the true mixing matrix and its estimate in independent component analysis. This bound applies to all algorithms that employ a prewhitening. Our analysis allows one to assess the contribution to the overall error of the partial estimation errors on the components of the singular value decomposition of the mixing matrix. The bound indicates the performance that can theoretically be achieved. It is actually reached for sufficiently high signaltonoise ratios by good algorithms. This is illustrated by means of a numerical experiment. A smallerror analysis allows to express the bound on the average precision in terms of the secondorder statistics of the estimator of the signal covariance. Index Terms—Eigenvalue decomposition (EVD), higher order statistics (HOS), independent component analysis (ICA), principal component analysis. I.