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
苏然 1雷英杰 1李繁华1
作者信息
- 1. 中北大学 数学学院,山西 太原 030051
- 折叠
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.
Abstract
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Key words
inverse eigenvalue problems/conic/sequential principal submatrices/extreme eigenvalues/arrow banded matrix引用本文复制引用
基金项目
山西省自然科学基金(201801D121153)
山西省基础研究计划(202203021211088)
出版年
2024
国家科技期刊平台
NSTL
万方数据