Orthogonal tensor decompositions

被引：268

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

页码：243 / 255

页数：13

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