An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors
An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors
复制标题
张量的特征值定位集，用于确定张量的正（半）定性
DOI：
10.1080/03081087.2015.1049582
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发表时间：
2016-04-01
影响因子：
1.1
通讯作者：
Li, Yaotang
中科院分区：
文献类型：
--
作者：
Li, Chaoqian;Li, Yaotang
给出了一个新的张量特征值局部化集，并证明了它比[Qi L.真实的超对称张量的本征值。J. Symbolic Comput. 2005;40：1302-1324]和[Li CQ，Li YT，Kong X.张量的新特征值包含集。编号。Linear Algebra Appl.2014;21：39-50]。在此基础上，我们给出了张量正定性的两个可检验的充分条件和张量半正定性的两个可检验的充分条件。
A new eigenvalue localization set for tensors is given, and proved to be tighter than those in [Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 2005;40:1302-1324] and [Li CQ, Li YT, Kong X. New eigenvalue inclusion sets for tensors. Numer. Linear Algebra Appl. 2014;21:39-50]. Based on this set, we give two checkable sufficient conditions of the positive definiteness of tensors, and two checkable sufficient conditions of the positive semi-definiteness of tensors.