On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

Abstract

Consider an $n \times n$ matrix polynomial $P(λ)$. An upper bound for a spectral norm distance from $P(λ)$ to the set of $n \times n$ matrix polynomials that have a given scalar $μ\in\mathbb{C}$ as a multiple eigenvalue was recently obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modification method is implemented and its efficiency is verified by an illustrative example.