Tensor logarithmic norm and its applications

被引：20
|
作者：
Ding, Weiyang [1 ]
Hou, Zongyuan [1 ]
Wei, Yimin [1 ,2 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2016年 / 23卷 / 06期
基金：
中国国家自然科学基金;
关键词：
logarithmic norm; stability of dynamical systems; tensor norm; tensor eigenvalue; spectral abscissa; tensor pair; PERRON-FROBENIUS THEOREM; SHIFTED POWER METHOD; LARGEST EIGENVALUE;
D O I：
10.1002/nla.2064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi-norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright (c) 2016 John Wiley & Sons, Ltd.
引用
收藏
页码：989 / 1006
页数：18
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