Rank-one approximation to high order tensors

被引：313
|
作者：
Zhang, T
Golub, GH
机构：
[1] IBM Corp, Thomas J Watson Res Ctr, Yorktown Hts, NY 10598 USA
[2] Stanford Univ, Sci Comp & Computat Math Program, Stanford, CA 94305 USA
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2001年 / 23卷 / 02期
关键词：
singular value decomposition; low-rank approximation; tensor decomposition;
D O I：
10.1137/S0895479899352045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.
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页码：534 / 550
页数：17
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