https://hal.inria.fr/hal-00907534Hladïk, MilanMilanHladïkCU - Charles University [Prague]Daney, DavidDavidDaneyCOPRIN - Constraints solving, optimization and robust interval analysis - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTechTsigaridas, EliasEliasTsigaridasCS - Department of Computer Science [Aarhus] - Aarhus University [Aarhus]Characterizing and Approximating Eigenvalue Sets of Symmetric Interval MatricesHAL CCSD2011EigenvalueEigenvalue boundsInterval analysisInterval matrixSymmetric matrix[INFO.INFO-RB] Computer Science [cs]/Robotics [cs.RO]Daney, David2013-11-21 13:50:152023-03-15 08:58:092013-11-21 13:50:15enJournal articles10.1016/j.camwa.2011.08.0281We 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.