THE BEST RANK-1 APPROXIMATION OF A SYMMETRIC TENSOR AND RELATED SPHERICAL OPTIMIZATION PROBLEMS

被引：71
作者：
Zhang, Xinzhen [1 ]
Ling, Chen [2 ]
Qi, Liqun [3 ]
机构：
[1] Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China
[2] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
[3] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2012年 / 33卷 / 03期
基金：
中国国家自然科学基金;
关键词：
symmetric tensor; the best rank-1 approximation; the best symmetric rank-1 approximation; power algorithm; POLYNOMIAL OPTIMIZATION; ORDER; SQUARES;
D O I：
10.1137/110835335
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show that for a symmetric tensor, its best symmetric rank-1 approximation is its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 approximation ratio of a symmetric tensor is given. Furthermore, a higher order polynomial spherical optimization problem can be reformulated as a multilinear spherical optimization problem. Then, we present a modified power algorithm for solving the homogeneous polynomial spherical optimization problem. Numerical results are presented, illustrating the effectiveness of the proposed algorithm.
引用
收藏
页码：806 / 821
页数：16
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