一类张量特征值反问题的可解性条件  

Solvability conditions for a class of tensor inverse eigenvalue problems

作　　者：代丽芳[1] 梁茂林[1] 冉延平[1] DAI Li-fang;LIANG Mao-lin;RAN Yan-ping(School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,Gansu,China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《山东大学学报（理学版）》2021年第6期95-102,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11961057);甘肃省高等学校科研基金资助项目(2018B-48);天水师范学院创新能力提升基金资助项目(CXT2019-36)。

摘　　要：利用张量Moore-Penrose广义逆的性质,得到Einstein积意义下Hermitian张量特征值反问题的可解性条件及其通解表达式。同时,对于任意给定张量,考虑上述反问题约束下的最佳逼近问题,得到它的唯一解表达式。给出的数值试验证实了这些结果的可行性。Using the properties of Moore-Penrose generalized inverses of tensors,the solvability conditions for the existence of the solution to the inverse eigenvalue problem of Hermitian tensors with Einstein product,as well as the general solution,are obtained.Meanwhile,the unique solution to the associated tensor approximation problem for any given tensor is given.The performed numerical results illustrate the feasibility of these results.

关 键 词：Hermitian张量 特征值反问题 MOORE-PENROSE广义逆 最佳逼近 

分 类 号：O241.6[理学—计算数学]