TY  - THES
AB  - The exact computation of an operator's spectrum is only possible in rare cases and its high susceptibility to perturbations poses a substantial challenge for approximations. This thesis delves into various approaches aimed at addressing this problem, utilizing spectral supersets such as the pseudospectrum and the quadratic numerical range as key tools. A new method for enclosing the pseudospectrum of a linear operator via the computable intersection of sets which are expressed in terms of the numerical ranges of shifted inverses of approximating matrices is introduced. The result is illustrated by means of the advection-diffusion, the Hain-Lüst and a Stokes-type operator. Moreover, a novel algorithm for the computation of the quadratic numerical range that is based on the maximization of a purposefully tailored objective function is presented. Numerous examples showcase that this computational technique outperforms the prevailing random vector sampling approach in both the quality of the produced images and computational speed.
AU  - Vorberg, Lukas
CY  - Wuppertal
DA  - 2024
DO  - 10.25926/BUW/0-197
DP  - Bergische Universität Wuppertal
LA  - eng
N1  - Tag der Verteidigung: 14.02.2024
N1  - Gesehen am 13.05.2024
N1  - Bergische Universität Wuppertal, Dissertation, 2024
PB  - Veröffentlichungen der Universität
PY  - März 2024
SP  - 1 Online-Ressource (xiv, 113 Seiten)
T2  - Mathematik und Informatik
TI  - The computation of spectral supersets of linear operators in Hilbert spaces
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:468-2-1996
Y2  - 2025-04-27T12:21:50
ER  -