Pseudospectra for matrix pencils and stability of equilibria

Abstract

The concept of "{pseudospectra for matrices, introduced by Trefethen and his co-workers, has been studied extensively since 1990. In this paper, "{ pseudospectra for matrix pencils, which are relevant in connection with generalized eigenvalue problems, are considered. Some properties as well as the practical computation of "{pseudospectra for matrix pencils will be discussed. As an application, we demonstrate how this concept can be used for investigating the asymptotic stability of stationary solutions to time-dependent ordinary or partial dierential equations; two cases, based on Burgers' equation, will be shown.