Characterizing and approximating eigenvalue sets of symmetric interval matrices |
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| Authors: | Milan Hladí k,David Daney,Elias Tsigaridas |
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| Affiliation: | aCharles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám. 25, 11800, Prague, Czech Republic;bINRIA Sophia-Antipolis Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France;cComputer Science Department, Aarhus University, Denmark |
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| 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. |
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| Keywords: | Interval matrix Symmetric matrix Interval analysis Eigenvalue Eigenvalue bounds |
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