Abstract
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.
Original language | English (US) |
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Pages (from-to) | 534-550 |
Number of pages | 17 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 23 |
Issue number | 2 |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
Keywords
- Low-rank approximation
- Singular value decomposition
- Tensor decomposition
ASJC Scopus subject areas
- Analysis