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Rank-One Approximation to High Order Tensors
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.
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Cited by
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Denton, R., Zaremba, W., Bruna, J., LeCun, Y., & Fergus, R. (2014) · arXiv · doi:10.48550/arxiv.1404.0736 · Cited by 1,414
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Metadata
- Authors
- Zhang, T., & Golub, G. H.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2001-01
- Volume
- 23
- Issue
- 2
- Pages
- 534-550
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2002598080
- Cited by
- 430
- References
- 0
- FWCI
- 1.87
- Type
- journal article
- Language
- en
- Open access
- closed
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