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A note on the normwise perturbation theory for the regular generalized eigenproblem

✍ Scribed by Valérie Frayssé; Vincent Toumazou

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 95 KB
Volume: 5
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199801/02)5:1<1::aid-nla121>3.0.co;2-x

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✦ Synopsis

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.