非对称矩阵的病态特征向量的约化

1.引言 关于密集特征值与其病态特征向量之间的内在联系,Varah(1970),Wilkinson(1972及1984)和Kahan(1970)曾经研究过.Varah(1970)最先指出:若矩阵A具有二阶以上的Jordan块,且当A加上一个扰动矩阵(?=A+E)则相似于对角阵时,其相似变换矩阵是病态的(即变换矩阵各列几乎线性相关).Varah对于病态的程度,给予了数

REDUCTION OF ILL-CONDITIONED EIGENVECTORS OF AN UNSYMMETRIC MATRIX

In this paper, we attempt to describe the relation between the clustered eigenvalues andthe ill-conditioned eigenvectors of a certain matrix, and to study how the ill-conditioned eigen-vectors occur. The general method reducing the ill-conditioned eigenvectors to the wellcondi-tioned ones is to add a tiny matrix E to the original matrix. In this paper, the construction ofthis matrix E is given. It is an expansion of Wilkinson and Kahan's work. The effect of themethod is shown by an example.