# Milan Hladík's Publications:

## Bounds on eigenvalues of real and complex interval matrices

Milan Hladík. Bounds on eigenvalues of real and complex interval matrices. * Appl. Math. Comput.*, 219(10):5584–5591, 2013.

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### Abstract

We present a cheap and tight formula for bounding real and imaginary parts of eigenvalues of real or complex interval matrices. It outperforms the classical formulae not only for the complex case but also for the real case. In particular, it generalizes and improves the results by Rohn (1998) and Hertz (2009). The main idea behind is to reduce the problem to enclosing eigenvalues of symmetric interval matrices, for which diverse methods can be utilized. The result helps in analysing stability of uncertain dynamical systems since the formula gives sufficient conditions for testing Schur and Hurwitz stability of interval matrices. It may also serve as a starting point for some iteration methods.

### BibTeX

@article{Hla2013a,
author = "Milan Hlad\'{\i}k",
title = "Bounds on eigenvalues of real and complex interval matrices",
journal = "Appl. Math. Comput.",
fjournal = "Applied Mathematics and Computation",
volume = "219",
number = "10",
pages = "5584-5591",
year = "2013",
issn = "0096-3003",
doi = "10.1016/j.amc.2012.11.075",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.amc.2012.11.075",
abstract = "We present a cheap and tight formula for bounding real and imaginary parts of eigenvalues of real or complex interval matrices. It outperforms the classical formulae not only for the complex case but also for the real case. In particular, it generalizes and improves the results by Rohn (1998) and Hertz (2009). The main idea behind is to reduce the problem to enclosing eigenvalues of symmetric interval matrices, for which diverse methods can be utilized. The result helps in analysing stability of uncertain dynamical systems since the formula gives sufficient conditions for testing Schur and Hurwitz stability of interval matrices. It may also serve as a starting point for some iteration methods.",
keywords = "Interval matrix, Interval analysis, Eigenvalue bounds",
}

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