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arXiv · 1401.0482

Nearest matrix with prescribed eigenvalues and its applications

Esmaeil Kokabifar·Ghasem Barid Loghmani·S. M. Karbassi
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Abstract

Consider $n \times n$ matrix $A$ and a set $\Lambda$ 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 $\Lambda$ and constructed a perturbation matrix $\Delta$ with minimum spectral norm such that $A+\Delta$ had $\Lambda$ in its spectrum. This paper presents an easy practical computational method for constructing the optimal perturbation $\Delta$ by extending necessary definitions and lemmas of previous works. Also, some conceivable applications of this issue are provided.

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Esmaeil Kokabifar, Ghasem Barid Loghmani, S. M. Karbassi. 2014-01-02. Nearest matrix with prescribed eigenvalues and its applications. https://arxiv.org/abs/1401.0482

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