NAFeb 18, 2015
Nearest matrix with prescribed eigenvalues and its applicationsEsmaeil Kokabifar, Ghasem Barid Loghmani, S. M. Karbassi
Consider $n \times n$ matrix $A$ and a set $Λ$ consisting of $k \le n$ prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from $A$ to the 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 extending necessary definitions and lemmas of previous works. Also, some conceivable applications of this issue are provided.