两类对称箭状矩阵的广义逆特征值问题  

Generalized Inverse Eigenvalue Problems for Two Kinds of Symmetric Arrow Matrix

作　　者：崔萌 雷英杰[1] CUI Meng;LEI Yingjie(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）》2022年第6期488-492,497,共6页Journal of North University of China(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(201801D1 21153)。

摘　　要：研究了两类具有不同结构的对称箭状矩阵的广义逆特征值问题.通过对问题Ⅰ与问题Ⅱ的解答来研究这两类矩阵的构造问题,将路径图与扫帚图推广得到本文研究的两类矩阵所对应的图.两个问题均利用了箭型矩阵及Jacobi矩阵的相关性质,将逆问题转换为求解线性方程组的问题,最终分别求解出两个问题有唯一解的充分必要条件,并得到了矩阵构造的实现过程.此外,问题Ⅰ与问题Ⅱ均给出构造广义矩阵的数值算法,通过两个具体的低阶矩阵实例的数值模拟,验证了问题Ⅰ与问题Ⅱ解的正确性.The generalized inverse eigenvalue problems of two symmetric arrow matrices with different structures were studied. By solving problem I and problem II, the construction of these two kinds of matrices was studied. The graphs corresponding to the two kinds of matrices in this paper was obtained by extending path graph and broom graph. By using the properties of arrow matrix and Jacobi matrix, the inverse problem was converted to the problem of solving linear equations. Finally, the necessary and sufficient conditions for the unique solution of the two problems were solved respectively, and the implementation process of matrix construction was obtained. In addition, problems Ⅰ and Ⅱ give numerical algorithms for constructing generalized matrices, and through the numerical simulation of two specific low-order matrix examples, the correctness of the solution of problem I and problem Ⅱ was verified.

关 键 词：特征对 逆特征值 箭状矩阵 数值算法 

分 类 号：O157[理学—数学]