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

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

Numerical Analysis 2015-05-26 v2

Authors: E. Kokabifar , G. B. Loghmani , P. J. Psarrakos , S. M. Karbassi

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.

Keywords

distance sets random matrix theory upper bounds

Cite

@article{arxiv.1405.2093,
  title  = {On the distance from a matrix polynomial to matrix polynomials with $k$ prescribed distinct eigenvalues},
  author = {E. Kokabifar and G. B. Loghmani and P. J. Psarrakos and S. M. Karbassi},
  journal= {arXiv preprint arXiv:1405.2093},
  year   = {2015}
}

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

Abstract

Keywords

Cite

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