A note on the normwise perturbation theory for the regular generalized eigenproblem
A note on the normwise perturbation theory for the regular generalized eigenproblem
复制标题
关于正则广义本征问题的范态微扰理论的注记
DOI：
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发表时间：
1998
影响因子：
4.3
通讯作者：
V. Toumazou
中科院分区：
文献类型：
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作者：
V. Frayssé;V. Toumazou
本文给出了正则广义特征值问题Ax = λBx的范数扰动理论，其中λ是半单的有限特征值，它不同于经典的弦范数分析[9].对于矩阵A和B中的独立扰动，给出了一个后向误差和一个条件数。最佳向后误差的概念只与一个特征值进行了讨论。© 1998 John Wiley & Sons，Ltd.
In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = λBx, when λ is a semi-simple and finite eigenvalue, which departs from the classical analysis with the chordal norm [9]. A backward error and a condition number are derived for a choice of flexible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error associated with an eigenvalue only is also discussed. © 1998 John Wiley & Sons, Ltd.