On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
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- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 21 (4) , 1324-1342
- https://doi.org/10.1137/s0895479898346995
Abstract
In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely, the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value decomposition (SVD); however, this approach does not have a straightforward multilinear counterpart. We discuss higher-order generalizations of the power method and the orthogonal iteration method.Keywords
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