Pseudospectra localizations and their applications
Vladimir Kostić, Ljiljana Cvetković, Dragana Lj. Cvetković · Numerical Linear Algebra with Applications · 2015
Summary Usefulness of spectral localizations in analysis of various matrix properties, such as stability of dynamical systems, has led us to derive a pseudospectra localization technique using the ideas that come from diagonally dominant matrices. In such way, many theoretical and practical applications of pseudospectra (robust stability, transient behavior, nonnormal dynamics, etc.) can be linked with specific relationships between matrix entries. This allows one to understand certain phenomena that occur in practice better, as we show for the realistic model of soil energetic food web. The novelty of the presented results, therefore, lies not only in new mathematical formulations but also in the conceptual sense because it links stability with empirical data and their uncertainty limitations. Copyright © 2015 John Wiley & Sons, Ltd.