矩阵特征值的一类新的包含域

A class of new inclusion regions for eigenvalues of matrices

用盖尔圆盘定理来估计矩阵的特征值是一个经典的方法,这种方法仅利用矩阵的元素来确定特征值的分布区域.本文利用相似矩阵有相同的特征值这一理论,得到了矩阵特征值的一类新的包含域,它们与盖尔圆盘等方法结合起来能提高估计的精确度.

It is a classical method to use the Gersgorin-disc theorem to estimate eigenvalues of a matrix.This method only uses elements of matrix to identify the distribution of eigenvalues.In this paper,a class of new inclusion regions,based on the fact that the similar matrices have same eigenvalues,are presented.The accuracy for estimating eigenvalues will be improved if one combines the results with the Gersgorin-disc theorems.