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Preprint 07-2012

On best rank one approximation of tensors

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Author(s) : Shmuel Friedland , Volker Mehrmann , Renato Pajarola , Susanne Suter

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 07-2012

MSC 2000

15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor products

Abstract :
In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called 'alternating singular value decomposition'. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. Finally, we introduce a new simple Newton-type method for speeding up the convergence of alternating methods near the optimum. We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.

Keywords : Singular value decomposition, rank one approximation, alternating least squares, Newton's method

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