Orthogonal tensor decompositions

被引：269
|
作者：
Kolda, TG [1 ]
机构：
[1] Sandia Natl Labs, Computat Sci & Math Res Dept, Livermore, CA 94551 USA
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2001年 / 23卷 / 01期
关键词：
tensor decomposition; singular value decomposition; principal components analysis; multidimensional arrays;
D O I：
10.1137/S0895479800368354
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We explore the orthogonal decomposition of tensors ( also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl., 269 (1998), pp. 307-329].
引用
收藏
页码：243 / 255
页数：13
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