On pseudospectra of matrix polynomials and their boundaries

@article{Boulton2008OnPO,
title={On pseudospectra of matrix polynomials and their boundaries},
author={Lyonell Boulton and Peter Lancaster and Panayiotis Psarrakos},
journal={Math. Comput.},
year={2008},
volume={77},
pages={313-334}
}

In the first part of this paper (Sections 2–4), the main concern is with the boundary of the pseudospectrum of a matrix polynomial and, particularly, with smoothness properties of the boundary. In the second part (Sections 5–6), 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.