A note on the sensitivity analysis of simple generalized eigenvalues

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Abstract

In this paper, we investigated the sensitivity and second-order perturbation expansions for simple generalized eigenvalues of a parameter-dependent analytic complex matrix pair. Our findings extended the perturbation analysis established by Sun (1985), which originally focused on simple eigenvalues. These results provided a theoretical foundation for applying Newton-type methods to generalized inverse eigenvalue problems.

Keywords

generalized eigenvalues / sensitivity analysis / generalized inverse eigenvalue problem

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