Nearest matrix with prescribed eigenvalues and its applications

Consider an n×nn×n matrix AA and a set ΛΛ consisting of k≤nk≤n prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from AA to the set of matrices whose spectra included specified set ΛΛ and constructed a perturbation matrix ΔΔ with minimum spectral norm such that A+ΔA+Δ had ΛΛ in its spectrum. This paper presents an easy practical computational method for constructing the optimal perturbation ΔΔ by improving and extending the methodology, necessary definitions and lemmas of previous related works. Also, some conceivable applications of this issue are provided.