A Counterexample to the Possibility of an Extension of the Eckart-Young Low-Rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition

Authors:
Tamara G. Kolda
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2002

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Abstract

Earlier work has shown that no extension of the Eckart--Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart--Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243--355].