Nearest matrix with prescribed eigenvalues and its applications

2014/01/02 by E. Kokabifar, Kokabifar, Esmaeil, Ghasem Barid Loghmani +3 · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Statistical and numerical algorithms #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1401.0482

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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