New pseudospectra localizations with application in ecology and vibration analysis

It is well-known that theory of pseudospectra has many important theoretical and practical applications, (for example, robust stability, transient behavior, nonnormal dynamics). It is also well-known that computational methods for pseudospectra determination are very costly for large matrices. Hence, it is necessary to find good, but relatively cheap, pseudospectra localizations. In this paper we derive some new pseudospectra localization sets, and compare them with the known ones, using relevant numerical examples arising in applications in ecology and vibration analysis. The new sets keep numerical complexity of the Pseudo-Geršgorin localization sets, but produce tighter results that can be compared to much more numerically complex localizations such as Pseudo-Brauer sets and Pseudo-CKV sets.