# On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors

@article{Lathauwer2000OnTB, title={On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors}, author={Lieven De Lathauwer and Bart De Moor and Joos Vandewalle}, journal={SIAM J. Matrix Anal. Appl.}, year={2000}, volume={21}, pages={1324-1342} }

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…

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