矩阵对(A,B)广义特征值定位算法  

AN ALGORITHM FOR EMBRACING THE SPECTRUM OF A MATRIX PENCIL (A,B) ON THE COMPLEX PLANE

作　　者：蔡大用[1] 

机构地区：[1]清华大学

出　　处：《高等学校计算数学学报》1993年第4期381-386,共6页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家基础性研究攀登项目

摘　　要：0 引言 设A,B为给定的两个N×N实矩阵,满足det(A—λB)=0的全体复数λ构成的集合称为矩阵对(A,B)的谱,并记为σ(A,B)。在很多工程实际问题中往往需要估计出复平面指定区域D上(A,B)广义特征值的个数(包含重数)。当某个λ_1∈σ(A,B)有较高的代数重数,或者σ(A,B)的元素在复平面上以“成堆”方式分布时(即某些σ(A,B)In this paper, an algorithm for embracing the spectrum of a matrix pencil (A,B) on the complex plane is given, which is based on the well-known principle of logarithm argument in complex analysis. An effective method for evaluating det(A-λB) and its derivative is deduced. The numerical examples show that the algorithm is useful for many practical purposes.

关 键 词：矩阵对 广义特征值 定位算法 

分 类 号：O241.6[理学—计算数学]