实对称区间矩阵特征值确界的交错定理及其应用  

Interlacing Theorem of Eigenvalue Supremum of the Real Symmetric Interval Matrices and Its Application

作　　者：成龙 李耀堂[2] CHENG Long;LI Yaotang(School of Mathematics and Computer Science,Chongqing University of International Business and Economics,Chongqing 401520,China;School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]重庆对外经贸学院数学与计算机学院,重庆401520 [2]云南大学数学与统计学院,云南昆明650091

出　　处：《应用数学》2024年第1期52-62,共11页Mathematica Applicata

基　　金：国家自然科学基金(11861077);重庆对外经贸学院研究项目(KYZK202311)。

摘　　要：本文将实对称矩阵特征值的交错定理推广到实对称区间矩阵,给出了实对称区间矩阵特征值确界的交错定理,并应用该定理构造了估计实对称三对角区间矩阵特征值界的算法.文中数值例子表明,本文所给算法与一些现有算法相比在使用范围、计算精度和计算量等方面都具有一定的优越性.In this paper,the interlacing theorem of eigenvalues of the real symmetric matrices is extended to the real symmetric interval matrices,the interlacing theorem of eigenvalues supremum of real symmetric interval matrices is given,and a algorithm of eigenvalues bounds of real symmetric tridiagonal interval matrices is constructed by using the theorem.The numerical examples show that the algorithm presented in this paper has certain advantages over some existing algorithms in terms of application scope,calculation accuracy and calculation workload.

关 键 词：实对称矩阵 实对称区间矩阵 实对称三对角区间矩阵 特征值 特征值区间 交错定理 

分 类 号：O241[理学—计算数学]