A counterexample to the possibility of an extension of the Eckart-Young low-rank approximation theorem for the orthogonal rank tensor decomposition

被引：52
作者：
Kolda, TG [1 ]
机构：
[1] Sandia Natl Labs, Comp Sci & Math Res Dept, Livermore, CA 94551 USA
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2003年 / 24卷 / 03期
关键词：
singular value decomposition; principal components analysis; multidimensional arrays; higher-order tensor; multilinear algebra;
D O I：
10.1137/S0895479801394465
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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].
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收藏
页码：762 / 767
页数：6
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