张量Z-特征值的最优参数定位区间及其应用  

An optimal parameter localization interval of the Z-eigenvalues of tensors and its application

作　　者：石求化 赵建兴 SHI Qiuhua;ZHAO Jianxing(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《延边大学学报(自然科学版)》2025年第1期62-65,共4页Journal of Yanbian University(Natural Science Edition)

基　　金：国家自然科学基金项目(62162012).

摘　　要：研究了张量Z-特征值的定位及其应用问题.首先利用张量Z-特征值的一个已含有参数定位区间,并通过选取最优参数得到了其在最优参数下的定位区间;其次,利用该最优参数所得的定位区间给出了一个判定偶次齐次多元多项式正定性的条件;最后,通过数值算例验证了所得结果的有效性。The localization and its application of the Z-eigenvalues of a tensor is researched.Firstly,by using an existing localization interval with parameters of the Z-eigenvalues of a tensor and by selecting the optimal parameters,a localization interval having optimal parameters is derived.And then,using this localization interval derived by this optimal parameters,a criterion for judging the positive definiteness of an even homogeneous multivariate polynomials is given.Finally,the effectiveness of the obtained theoretical results is verified by a numerical example.

关 键 词：对称张量 Z-特征值 定位区间 多元多项式 正定性 

分 类 号：O151.23[理学—数学]