Milan Hladík, David Daney, and Elias P. Tsigaridas. Characterizing and approximating eigenvalue sets of symmetric interval matrices. Comput. Math. Appl., 62(8):3152–3163, 2011.
[PDF] [gzipped postscript] [postscript] [HTML]
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries are perturbed, with perturbations belonging to some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guarantee exactness. We illustrate our approach by several examples and numerical experiments.
@article{HlaDan2011c,
author = "Milan Hlad\'{\i}k and David Daney and Elias P. Tsigaridas",
title = "Characterizing and approximating eigenvalue sets of symmetric interval matrices",
journal = "Comput. Math. Appl.",
fjournal = "Computers \& Mathematics with Applications",
volume = "62",
number = "8",
pages = "3152-3163",
year = "2011",
doi = "10.1016/j.camwa.2011.08.028",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.camwa.2011.08.028",
abstract = "We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries are perturbed, with perturbations belonging to some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guarantee exactness. We illustrate our approach by several examples and numerical experiments.",
keywords = "interval matrix, symmetric matrix, interval analysis, eigenvalue bounds",
}
Generated by bib2html.pl (written by Patrick Riley ) on Wed Oct 23, 2024 08:16:44