Localization of the matrix spectrum and Lyapunov type equations
https://doi.org/10.26907/2949-3919.2023.4.49-66
Abstract
The problems on the location of the matrix spectrum inside or outside domains bounded by ellipses or parabolas are studied. Special Lyapunov-type equations are connected with these problems. Theorems about the unique solvability of such equations are proved. Conditions for perturbations of matrix entries are obtained, which guarantee that the spectra of the perturbed matrices belong to the specified domains as well.
Keywords
Lyapunov-type matrix equations,
Krein’s theorem,
localization of the matrix spectrum,
problems on spectral perturbations
Supporting agencies: The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).
About the Authors
G. V. Demidenko
Sobolev Institute of Mathematics;
Novosibirsk State University
Russian Federation
Russian Federation
Gennadii Vladimirovich Demidenko
4 Acad. Koptyug Avе., Novosibirsk 630090, Russia;
1 Pirogov str., Novosibirsk 630090, Russia
Zongshun Wang
Novosibirsk State University
Russian Federation
Russian Federation
Wang Zongshun
1 Pirogov str., Novosibirsk 630090, Russia
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Review
For citations:
Demidenko G.V., Wang Z. Localization of the matrix spectrum and Lyapunov type equations. Mathematics and Theoretical Computer Science. 2023;1(4):49-66. (In Russ.) https://doi.org/10.26907/2949-3919.2023.4.49-66
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