Rank-one approximation to high order tensors

被引：321

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.

引用

页码：534 / 550

页数：17

共 31 条

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