两类非对称双箭型矩阵的广义逆谱问题  

Generalized Inverse Spectrum Problems for Two Kinds of Nonsymmetric Doubly Arrow Matrix

作　　者：苏然 雷英杰[1] 李繁华 SU Ran;LEI Yingjie;LI Fanhua(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第2期158-162,169,共6页Journal of North University of China(Natural Science Edition)

基　　金：山西省基础研究计划资助项目(202203021211088)。

摘　　要：针对两类非对称双箭型矩阵的广义逆谱问题,本文先将两类矩阵的两组特征对作为其特征数据,然后利用矩阵元素间具有的函数关系、线性关系及箭型矩阵的相关性质,将两类矩阵的逆谱问题转换为求解线性方程组的问题,进而实现了两类矩阵的重构。本文给出了该问题有唯一解的充分必要条件以及问题构造的算法,并通过相应数值实例验证了所得结果。The generalized inverse spectral problem of two types of nonsymmetric double-arrow matrices was studied in this paper.Firstly,two sets of eigenpairs of two types of matrices were used as their eigendata.Secondly,the inverse spectral problem of two types of matrices was converted into a problem of solving a system of linear equations by using the functional relationship between matrix elements,linear relationship and the related properties of arrow matrices,and then the reconstruction of two types of matrices was realized.Finally,the sufficient and necessary conditions for the problem to have a unique solution and the algorithm for the problem construction were given,and the results were verified by the corresponding numerical examples.

关 键 词：特征对 逆谱问题 箭型矩阵 线性关系 函数关系 

分 类 号：O157[理学—数学]