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Characterizing and Approximating Eigenvalue Sets of Symmetric Interval Matrices

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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https://hal.inria.fr/hal-00907534
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Submitted on : Thursday, November 21, 2013 - 1:50:15 PM
Last modification on : Thursday, January 20, 2022 - 5:31:27 PM

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Milan Hladïk, David Daney, Elias Tsigaridas. Characterizing and Approximating Eigenvalue Sets of Symmetric Interval Matrices. Computers & Mathematics with Applications, Elsevier, 2011, 62 (8), pp.3152--3163. ⟨10.1016/j.camwa.2011.08.028⟩. ⟨hal-00907534⟩

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