由非顺序主子阵和缺损广义特征对构造对称三对角矩阵

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (2): 10-21.

由非顺序主子阵和缺损广义特征对构造对称三对角矩阵

朱群娣, 洪平洲, 黄贤通

赣南师范大学数学与计算机科学学院,赣州,341000

出版日期:2016-06-30 发布日期:2020-09-29
基金资助:
中央财政支持地方高校发展专项基金—应用数学创新团队建设

Constructing a Symmetric Tridiagonal Matrix Based on Its Defective Generalized Eigenpair and Nonleading Principle Submatrix

Zhu Qundi, Hong Pingzhou, Huang Xiantong

College of Mathematics and Computer Science,Gannan Normal University,GanZhou 341000,Jiangxi Province,China

Online:2016-06-30 Published:2020-09-29

摘要/Abstract

摘要： 本文讨论形如AnX =λCnX 的方程,其中An是一个对称三对角矩阵,Cn是一个对角矩阵.对矩阵An进行3×3分块,给定An的一个非顺序主子阵Ar+1,r+s ,给定Cn和四个向量X1 = (x1,…,xr)＇,X3 = (xr+s+1,…,xn)＇,Y1 = (y1,…,yr)＇,Y3 = (yr+s+1,…,yn)＇和两个不同实数λ,μ,构造一个对称三对角矩阵An和两个向量X2 = (xr+1,…,xr+s)＇,Y2 = (yr+1,…,yr+s)＇,满足AnX =λCnX 和AnY =μCnY ,其中X = (X1＇,X2＇,X3＇)＇,Y = (Y1＇,Y2＇,Y3＇)＇.本文给出问题有解的条件,解的表达式和相应算法,并给出数值算例验证算法的有效性.

关键词: 对称三对角矩阵, 对角矩阵, 广义特征值反问题, 非顺序主子阵, 缺损广义特征对

Abstract: In this paper we consider the equation AnX =λCnX ,where Anis a symmetric tridiagonal matrix and Cnis a diagonal matrix.Regarding Anas a 3×3blocked matrix,given a(r+1)×(r+s)non-sequential principle submatrix of An ,given Cn ,four vectors X1 = (x1,…,xr)＇,X3=(xr+s+1,…,xn)＇,Y1 = (y1,…,yr)＇,Y3=(yr+s+1,…,yn)＇and two distinct real numbersλ,μ,we construct a symmetric tridiagonal matrix Anand two vectors X2 = (xr+1,…,xr+s)＇,Y2= (yr+1,…,yr+s)＇such that AnX =λCn X and AnY =μCn Y ,where X = (X1＇, X2＇,X3＇)＇,Y = (Y1＇,Y2＇,Y3＇)＇.The existence conditions such that the problem has a solution and the corresponding algorithm to find the solutions are given.A numerical example is presented to show the validity of the algorithm.

Key words: Symmetric tridiagonal matrix, Diagonal matrix, The inverse generalized eigenvalue problem, , Nonleading principle submatrix, Defective generalized eigenpair

朱群娣, 洪平洲, 黄贤通.

由非顺序主子阵和缺损广义特征对构造对称三对角矩阵 [J]. 数学理论与应用, 2016, 36(2): 10-21.

Zhu Qundi, Hong Pingzhou, Huang Xiantong. Constructing a Symmetric Tridiagonal Matrix Based on Its Defective Generalized Eigenpair and Nonleading Principle Submatrix[J]. Mathematical Theory and Applications, 2016, 36(2): 10-21.