对称周期Jacobi矩阵加箭型矩阵的广义逆谱问题  

Generalized Inverse Eigenvalue Problem of Symmetric Periodic Jacobi Matrix Plus 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：《山西大学学报（自然科学版）》2024年第3期564-570,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(201801D121153);山西省基础研究计划资助项目(202203021211088)。

摘　　要：研究了一类对称周期Jacobi矩阵加箭型矩阵的广义逆谱问题,利用几何学上圆锥曲线,对称周期Jacobi矩阵及箭型矩阵的相关性质,将该矩阵所有主子阵的极端特征值作为其特征数据,来重构此类箭状矩阵。最后得出该问题的解以及问题构造的算法与实例,验证了结果的准确性。In this paper,we study the generalized inverse spectrum problem for a class of symmetric periodic Jacobi matrices plus ar-row matrices.By using the geometric properties of conic curve,symmetric periodic Jacobi matrix and arrow matrix,the extreme ei-genvalues of all the principal submatrixes of the matrix are taken as their characteristic data to reconstruct this kind of arrow banded matrix.Finally,the solution of the problem is derived as well as the algorithm and examples of the problem construction,and the ac-curacy of the results is verified.

关 键 词：逆特征值问题 圆锥曲线 顺序主子阵 极端特征值 箭状矩阵 

分 类 号：O157[理学—数学]