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

Consider an$n\times n matrix polynomial P(\lambda). An upper bound for a spectral norm distance from P(\lambda) to the set of n \times n matrix polynomials that have a given scalar ? in C as a multiple eigenvalue was obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modified method is developed and its efficiency is verified by two illustrative examples. The proposed methodology can also be applied to general matrix polynomials.