On the distance from a matrix polynomial to matrix polynomials with k prescribed distinct eigenvalues
E. Kokabifar, Ghasem Barid Loghmani, Panayiotis Psarrakos, Seyed Mahdi Karbassi · Linear and Multilinear Algebra · 2016
Consider an matrix polynomial and a set consisting of distinct complex numbers. In this paper, a (weighted) spectral norm distance from to the matrix polynomials whose spectra include the specified set , is defined and studied. An upper and a lower bound for this distance are obtained, and an optimal perturbation of associated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds.