Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 23, Issue 2, Pages 534-550Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0895479899352045
Keywords
singular value decomposition; low-rank approximation; tensor decomposition
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The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.
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