Nearest matrix with prescribed eigenvalues and its applications

摘要

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