Since 1963
Sensitivity analysis of multiple eigenvalues and associated eigenvectors of quadratic eigenproblem
1
Faculty of Civil Engineering and Resource Management, AGH University of Cracow, Cracow, Poland
Submission date: 2024-11-21
Final revision date: 2025-02-20
Acceptance date: 2025-03-19
Online publication date: 2025-09-22
Corresponding author
Henryk Ciurej
Faculty of Civil Engineering and Resource Management, Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie, Al. Mickiewicza 30, 30-059 Kraków, Poland
Faculty of Civil Engineering and Resource Management, Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie, Al. Mickiewicza 30, 30-059 Kraków, Poland
KEYWORDS
TOPICS
ABSTRACT
The article is focused on the sensitivity of eigenvalues and eigenvectors in a quadratic eigenvalue problem with real matrices defining the problem under consideration and under the strong assumption that these matrices form a non-defective operator. The particular interest is the case of multiple eigenvalues and associated eigenvectors. Generally in such a case derivatives in the Fréchet sense do not exist, but only in the Gâteaux sense. The formulas of the directional differential in the closed matrix form were derived. A numerical example is shown.
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