Characterizing and approximating eigenvalue sets of symmetric interval matrices

Authors:
Milan Hladík;David Daney;Elias Tsigaridas
Affiliations:
Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám.25, 11800, Prague, Czech Republic and INRIA Sophia-Antipolis Méditerran&# ...;INRIA Sophia-Antipolis Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France;Computer Science Department, Aarhus University, Denmark
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 7
Cited 0

On the range of eigenvalues of an interval matrix

Computing
Interval matrices: singularity and real eigenvalues

SIAM Journal on Matrix Analysis and Applications
Matrix analysis and applied linear algebra

Matrix analysis and applied linear algebra
Interval analysis: theory and applications

Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Principal component analysis on interval data

Computational Statistics
An algorithm for addressing the real interval eigenvalue problem

Journal of Computational and Applied Mathematics
Bounds on Real Eigenvalues and Singular Values of Interval Matrices

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.09

Visualization

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.