TY - JOUR

T1 - Localization of the Matrix Spectrum and Lyapunov Type Equations

AU - Demidenko, G. V.

AU - Wang, Z.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).

PY - 2024/4

Y1 - 2024/4

N2 - 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.

AB - 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.

KW - Krein’s theorem

KW - Lyapunov-type matrix equations

KW - location of the matrix spectrum

KW - problems on spectral perturbations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85201799227&origin=inward&txGid=ac376440ed32dc92cf8c84e2cb3efaf7

UR - https://www.mendeley.com/catalogue/262a54b8-1f92-3ac6-a1a8-1d1248529e13/

U2 - 10.1134/S1995080224601358

DO - 10.1134/S1995080224601358

M3 - Article

VL - 45

SP - 1808

EP - 1818

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 4

ER -