Pseudospectra for matrix pencils and stability of equilibria

The concept of ε-pseudospectra for matrices, introduced by Trefethen and his coworkers, has been studied extensively since 1990. In this paper, ε-pseudospectra for matrix pencils, which are relevant in connection with generalized eigenvalue problems, are considered. Some properties as well as the practical computation of ε-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 differential equations; two cases, based on Burgers' equation, will be shown.

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