On Pseudospectra of Matrix Polynomials and their Boundaries

Abstract

In the first part of this paper, the main concern is with smoothness properties of the boundary of the pseudospectrum of a matrix polynomial. In the second part, results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials.

31 pages, 5 figures, recently submitted to Mathematics of Computation. In this revised version we have corrected some further typos and added an extra example