A note on the sensitivity analysis of simple generalized eigenvalues

Ming-chai Yu; Xing Chen; Wei Ma; Ming-chai Yu; Xing Chen; Wei Ma

doi:10.3934/era.2026292

Electronic Research Archive

2026, Volume 34, Issue 9: 6688-6701. doi: 10.3934/era.2026292

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Research article

A note on the sensitivity analysis of simple generalized eigenvalues

1.
School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
2.
School of Software Engineering, Nanyang Normal University, Nanyang 473061, China

Received: 21 May 2026 Revised: 21 July 2026 Accepted: 28 July 2026 Published: 06 August 2026

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.
- generalized eigenvalues,
- sensitivity analysis,
- generalized inverse eigenvalue problem
Citation: Ming-chai Yu, Xing Chen, Wei Ma. A note on the sensitivity analysis of simple generalized eigenvalues[J]. Electronic Research Archive, 2026, 34(9): 6688-6701. doi: 10.3934/era.2026292

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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.

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