一类张量特征值反问题的可解性条件

doi:10.6040/j.issn.1671-9352.0.2020.463

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 95-102.doi: 10.6040/j.issn.1671-9352.0.2020.463

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一类张量特征值反问题的可解性条件

代丽芳,梁茂林^*,冉延平

天水师范学院数学与统计学院, 甘肃天水 741001

发布日期:2021-06-03
作者简介:代丽芳(1981— ),女,硕士,讲师,研究方向为数值线性代数. E-mail:dailf2005@163.com*通信作者简介:梁茂林(1981— ),男,博士,副教授,研究方向为数值多重线性代数. E-mail:liangml2005@163.com
基金资助:
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)

Solvability conditions for a class of tensor inverse eigenvalue problems

DAI Li-fang, LIANG Mao-lin^*, RAN Yan-ping

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu, China

Published:2021-06-03

摘要/Abstract

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。

关键词: Hermitian张量, 特征值反问题, Moore-Penrose广义逆, 最佳逼近

Abstract: 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.

Key words: Hermitian tensors, inverse eigenvalue problem, Moore-Penrose generalized inverse, optimal approximation

中图分类号:

O241.6

代丽芳,梁茂林,冉延平. 一类张量特征值反问题的可解性条件[J]. 《山东大学学报(理学版)》, 2021, 56(6): 95-102.

DAI Li-fang, LIANG Mao-lin, RAN Yan-ping. Solvability conditions for a class of tensor inverse eigenvalue problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(6): 95-102.

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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

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