PSEUDOSPECTRA AND DYNAMICAL SYSTEMS APPLICATIONS

Abstract

This paper is devoted to describing and illustrating pseudospectra and the connections ofpseudospectra with related quantities for non-normal matrices, in particular, the distance to instability, the H norm, and distance to uncontrollability. Pseudospectra and related quantities became a standard tool in the1990s, with applications in mechanics, numerical analysis, operator theory, control theory, differential and integral equation. In all of this fields it has been found that in case of pronounced non-normality, eigenvalues and eigenvectors alone do not always reveal much about the aspects of the behavior of a matrix or operator that matter in applications, including phenomena of stability, convergence, and resonance, and that pseudoeigenvalues and pseudo-eigenvector may do better.