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arXiv · 1405.2093

On the distance from a matrix polynomial to matrix polynomials with $k$ prescribed distinct eigenvalues

E. Kokabifar·G. B. Loghmani·P. J. Psarrakos·S. M. Karbassi
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Abstract

Consider an $n\times n$ matrix polynomial $P(\lambda)$ and a set $\Sigma$ consisting of $k \le n$ distinct complex numbers. In this paper, a (weighted) spectral norm distance from $P(\lambda)$ to the matrix polynomials whose spectra include the specified set $\Sigma$, is defined and studied. An upper and a lower bounds for this distance are obtained, and an optimal perturbation of $P(\lambda)$ associated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds.

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E. Kokabifar, G. B. Loghmani, P. J. Psarrakos, S. M. Karbassi. 2014-05-08. On the distance from a matrix polynomial to matrix polynomials with $k$ prescribed distinct eigenvalues. https://arxiv.org/abs/1405.2093

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