On the distance from a normal matrix polynomial to the set of matrix   polynomials with a prescribed multiple eigenvalue
  This paper concerns the bounds for spectral norm distance from a normal matrix polynomial $P(\lambda)$ to the set of matrix polynomials that have $\mu$ as a multiple eigenvalue. Also construction of associated perturbations of $P(\lambda)$ is considered. 
Esmaeil Kokabifar and Ghasem Barid Loghmani
math.NA