Milan Hladík, David Daney, and Elias P. Tsigaridas. A filtering method for the interval eigenvalue problem. Appl. Math. Comput., 217(12):5236–5242, 2011.
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We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer approximation (superset) of the real eigenvalue set of an interval matrix, we propose a filtering method that iteratively improves the approximation. Even though our method is based on a sufficient regularity condition, it is very efficient in practice and our experimental results suggest that it improves, in general, significantly the initial outer approximation. The proposed method works for general, as well as for symmetric interval matrices.
@article{HlaDan2011b,
author = "Milan Hlad\'{\i}k and David Daney and Elias P. Tsigaridas",
title = "A filtering method for the interval eigenvalue problem",
journal = "Appl. Math. Comput.",
fjournal = "Applied Mathematics and Computation",
volume = "217",
number = "12",
pages = "5236-5242",
year = "2011",
doi = "10.1016/j.amc.2010.09.066",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.amc.2010.09.066",
abstract = "We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer approximation (superset) of the real eigenvalue set of an interval matrix, we propose a filtering method that iteratively improves the approximation. Even though our method is based on a sufficient regularity condition, it is very efficient in practice and our experimental results suggest that it improves, in general, significantly the initial outer approximation. The proposed method works for general, as well as for symmetric interval matrices.",
keywords = "interval matrix, symmetric matrix, interval analysis, eigenvalue bounds",
}
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