# On Matrix Nearness Problems: Distance to Delocalization

@article{Kostic2015OnMN, title={On Matrix Nearness Problems: Distance to Delocalization}, author={Vladimir Kostic and Agnieszka Miedlar and Jeroen J. Stolwijk}, journal={SIAM J. Matrix Anal. Appl.}, year={2015}, volume={36}, pages={435-460} }

In this paper we introduce a new matrix nearness problem that is intended to generalize the distance to instability. Due to its applicability in analyzing the robustness of eigenvalues with respect to the arbitrary localization sets (domains) in the complex plane, we call it the distance to delocalization. For the open left half-plane or the unit disk, the distance to the nearest unstable matrix is obtained as a special case. Following the theoretical framework of Hermitian functions and the…

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