Nearest matrix with prescribed eigenvalues and its applications
Abstract
Consider 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 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.
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