Repository: DepositOnce â€“ institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Kostic, Vladimir
AU - Miedlar, Agnieszka
AU - Stolwijk, Jeroen
PY - 2014
TI - On Matrix Nearness Problems: Distance to Delocalization
DO - 10.14279/depositonce-14595
UR - http://dx.doi.org/10.14279/depositonce-14595
PB - Technische UniversitÃ¤t Berlin
LA - en
AB - This paper introduces two new matrix nearness problems that are intended to generalize the distance to instability and the distance to stability. They are named the distance to delocalization and the distance to localization due to their applicability in analyzing the robustness of eigenvalues with respect to arbitrary localization sets (domains) in the complex plane. For the open left-half plane or the unit circle, the distance to the nearest unstable/stable matrix is obtained as a special case. Then, following the theoretical framework of Hermitian functions and the Lyapunov-type localization approach, we present a new Newton-type algorithm for the distance to delocalization (D2D) and study its implementations using both an explicit and an implicit computation of the desired singular values. Since our investigations are motivated by several practical applications, we will illustrate our approach on some of them. Furthermore, in the special case when the distance to delocalization becomes the distance to instability, we will validate our algorithms against the state of the art computational method.
KW - stability
KW - matrix nearness problems
KW - distance to instability
KW - distance to stability
KW - spectral abscissa
KW - stability radius
KW - $\eps$-pseudospectra
KW - Lyapunov stability test
KW - Hermitian functions
KW - Newton's method
ER -