Rank-one approximation to high order tensors (Q2784363)

The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by \textit{C. Eckart} and \textit{G. Young} [The approximation of one matrix by another of lower rank. Psychometrika 1, 211-218 (1939)], where they considered the problem of low-rank approximation to high order tensors, which the author call the multidimensional SVD. In this paper, the authors investigate certain properties of this decomposition as well as numerical algorithms. NEWLINENEWLINENEWLINESection 2 is equivalent rank-one formulations. In Section 3, the authors study orthogonal tensor decompositions. Section 4 contains algorithms: Generalized Rayleigh-Newton iteration; Alternating least squares method; and Jacobi Gauss-Newton procedure. Section 5 presents experimental results. The authors make conclusions in Section 6.