张量的一个新S-型特征值定位集及其应用  

A New S-type Eigenvalue Localization set for Tensors with Application

作　　者：焦爱全 张晓辉 潘利双 石立叶 JIAO Ai-quan;ZHANG Xiao-hui;PANG Li-shuang;SHI Li-ye(Department of Mathematical Sciences and Engineering,Hebei University Engineering,Handan 056002,China;Department of Mathematics,Handan College,Handan 056002,China;Science College,Shijiazhang University,Shijiazhang 050035,China)

机构地区：[1]河北工程大学数理科学与工程学院,河北邯郸056002 [2]邯郸学院数理学院,河北邯郸056002 [3]石家庄学院理学院,河北石家庄050035

出　　处：《数学的实践与认识》2020年第1期249-257,共9页Mathematics in Practice and Theory

基　　金：邯郸市科技局(1721211052-5);邯郸学院校级课题(2017230).

摘　　要：通过分裂集合N={1,2,…,n}为子集S及其补集S得到张量的一个比文献中Qi和Li等给出的定位集更小的新S-型特征值定位集,并由该定位集得到了张量正定性判定的一个充分条件和非负张量谱半径的一个更优上界.A new S-type eigenvalue localization set for tensors is given by breaking N={1,2,…,n} into a disjoint subset S and its complement S.It has been proved that the new set is tighter than those in Qi and Li.Based on this new set,we give a checkable sufficient condition for the positive(semi-)definiteness of tensors and an upper bound for the spectral radius of nonnegative tensors.

关 键 词：张量特征值 定位集 正定性 谱半径 

分 类 号：O151.21[理学—数学]