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Abstract:
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in 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 guaran- tee exactness. We illustrate our approach by several examples and numerical experiments.
BibTeX:
@article{HlDaTsi-cma-2011,
author = {Hlad\'{\i}k, Milan and Daney, David and Tsigaridas,
Elias},
title = {Characterizing and approximating eigenvalue sets of
symmetric interval matrices},
journal = {Comput. Math. Appl.},
issue_date = {October, 2011},
volume = 62,
number = 8,
month = oct,
year = 2011,
issn = {0898-1221},
pages = {3152--3163},
numpages = 12,
url = {http://hal.inria.fr/inria-00567385},
publisher = {Pergamon Press, Inc.},
address = {Tarrytown, NY, USA},
keywords = {Eigenvalue, Eigenvalue bounds, Interval analysis,
Interval matrix, Symmetric matrix},
abstract = "We consider the eigenvalue problem for the case
where the input matrix is symmetric and its entries
perturb in 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 guaran- tee exactness. We
illustrate our approach by several examples and
numerical experiments.",
}
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