Spectral portraits for matrix pencilsVal

Spectral portraits and pseudospectra have recently attracted the attention of many scientists as a tool of choice for investigating spectral properties of nonnormal matrices. Until now, most of the papers devoted to this topic were generally dealing with the standard eigenproblem Ax = x. However in practice, physical applications often give rise to generalized eigenproblems Ax = Bx. It is therefore natural to extend the notion of "-pseudospectrum and spectral portrait to matrix pencils (A; B). In this paper, we explain how to deene and compute spectral portraits for matrix pencils and we illustrate their importance on and example in Computational Fluid Dynamics.