P. J. Psarrakos

E. Kokabifar, G. B. Loghmani, P. J. Psarrakos et al.

Consider an $n\times n$ matrix polynomial $P(λ)$ and a set $Σ$ consisting of $k \le n$ distinct complex numbers. In this paper, a (weighted) spectral norm distance from $P(λ)$ to the matrix polynomials whose spectra include the specified set $Σ$, is defined and studied. An upper and a lower bounds for this distance are obtained, and an optimal perturbation of $P(λ)$ associated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds.

E. Kokabifar, G. B. Loghmani, P. J. Psarrakos

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.