Quadratic perturbation bounds for generalized eigenvalue problems

Details Quadratic perturbation bounds for generalized eigenvalue problems Quadratic perturbation bounds for generalized eigenvalue problems

2010-08-06

arxiv.org/abs/1008.1185v2

Mathematics

Numerical Analysis

This paper has been withdrawn by the author because refined results will be presented in a collaborative work

Scientific paper

We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results we provide a simple derivation of the first-order perturbation expansion of a multiple eigenvalue, whose trailing term is tighter than known results. We also present quadratic bounds for the non-Hermitian case.

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