连箭矩阵的逆谱问题  

Inverse spectrum problems of connected arrow matrix

作　　者：吉雁斐 雷英杰[1] JI Yanfei;LEI Yingjie(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《黑龙江大学自然科学学报》2022年第1期49-57,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(12071444)。

摘　　要：研究了两个关于图是密蜈蚣的连箭矩阵A_(3n)(即多个连续箭形矩阵组合而成的大型矩阵)重构的逆特征值问题,主要是从给定的部分特征数据出发,如矩阵的特征对和最大特征值,利用该矩阵顺序主子阵间的递推关系来实现。最后给出了该矩阵解的表达式以及数值模拟实例,验证了结果的准确性。Two inverse eigenvalue problems about the reconstruction of a continuous arrow matrix(that is, a large matrix composed of multiple connected arrow matrices) whose graph is a dense centipede are studied. It is mainly based on the given part of the characteristic data, such as the eigenpair and the maximal eigenvalue of the matrix, to realize it by using the recurrence relationship between sequential principal submatrices of the matrix. Finally, the expression of the matrix solution and numerical simulation examples are given to verify the accuracy of the results.

关 键 词：逆特征值问题 箭形矩阵 最大特征值 顺序主子阵 特征对 图矩阵 

分 类 号：O151.21[理学—数学]