On the best rank-1 approximation to higher-order symmetric tensors

被引：23
作者：
Ni, Guyan [1 ]
Wang, Yiju
机构：
[1] Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China
[2] Qufu Normal Univ, Sch Management Sci & Operat Res, Rizhao Shandong, Peoples R China
[3] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2007年 / 46卷 / 9-10期
基金：
中国国家自然科学基金;
关键词：
even-order tensors; rank-1; tensors; symmetric tensors;
D O I：
10.1016/j.mcm.2007.01.008
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we consider the best rank-1 approximation to higher-order symmetric tensors in the least-squares sense, and show that the best rank-1 approximation of a symmetric tensor with even order m can be determined by m/2 unit spheres and a best symmetric rank-1 approximation of a symmetric tensor with order 4 and dimension 2 is also its best rank-1 approximation. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1345 / 1352
页数：8
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