度为2的广义星图矩阵的逆特征值问题  

Inverse Eigenvalue Problems for Generalized Star Graph Matrix with Degree 2

作　　者：李繁华 雷英杰[1] 苏然 LI Fanhua;LEI Yingjie;SU Ran(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163-169,共7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：运用两种不同的方法对度为2的广义星图矩阵(一种特殊类型的树的矩阵)的逆特征值问题进行了深入研究。首先,引入了一种标记这种树的顶点的方案,以便以多种特殊形式表示相应的矩阵。然后,针对给定的两类不同的特征数据,将此类矩阵的逆特征值问题转化为线性方程组求解问题,得到了所研究问题有唯一解的充分必要条件。最后,给出了矩阵唯一解的表达式和相应的算法。通过数值模拟实例验证了结果的准确性。The inverse eigenvalue problems of generalized star graph matrices(matrices of a special kind of tree)with degree 2 were studied by using two methods.Firstly,a scheme for labeling the vertices of such a tree was introduced in order to express the corresponding matrices in a number of special forms.Then,inverse eigenvalue problem of matrix for the given two different kinds of eigendata was transformed into the solution of the system of linear equations,and the sufficient and necessary conditions for the problem to have a unique solution were obtained.Finally,an expression for the unique solution of the matrix was provided,and the numerical algorithms and examples were given to verify the accuracy of the results.

关 键 词：向量对 特征对 逆特征值问题 广义星图 图矩阵 

分 类 号：O157[理学—数学]