广义特征值的扰动界限(Ⅰ)

PERTURBATION BOUNDS FOR GENERALIZED EIGENVALUES(Ⅰ)

到目前为止,关于广义特征值的扰动,已经建立了一些界限估计,但一般正则对的扰动界限难以算出.首先,定义某些基本参数,并利用这些参数建立几个关于一般正则矩阵对的广义特征值的扰动定理.这些定理给出的扰动界限的上界估计,一般是可以算出的.

For the perturbation of generalized eigenvalues of generally regular matrix pairs, it isdifficult to estimate perturbation bounds in spite of the existing results. Some bounds to re-deem this defect are developed. Then, another version of Henrici type theorem is proved, fromwhich it deduces two upper bounds which could not be deduced from the previous one.