关于矩阵特征值问题向后误差分析的注记

A NOTE ON THE BACKWARD ERROR ANALYSIS FOR EIGENVALUE PROBLEMS

本文研究实矩阵关于复近似特征对的范数型向后误差．在复扰动情形,这个问题已被Higham 等学者解决．本文研究实扰动情形．结果表明,通常情况下,两种情形差别不大,但在某些情形,二者可以相差很大．作为推广,我们还讨论了矩阵多项式的相应问题．文中的一个结果部分地解决了D．J．Higham和N．J．Higham 1999年提出的一个待解决的问题．

This paper deals with backward errors of a real matrix with respect to an approximate complex eigenpair. Both complex and real perturbations cases are considered. The conclusion is that, in general there are no essential difference between the two cases, but there are large differences in some situations. This extends to polynomial eigenvalue problems. As a by-product, a problem raised by Higham and Higham is partially solved.