Computing the spectral decomposition of interval matrices and a study on interval matrix powers

0541295 - ÚI 2022 RIV US eng J - Journal Article
Hartman, David - Hladík, M. - Říha, D.
Computing the spectral decomposition of interval matrices and a study on interval matrix powers.
Applied Mathematics and Computation. Roč. 403, August 2021 (2021), č. článku 126174. ISSN 0096-3003. E-ISSN 1873-5649
Institutional support: RVO:67985807
Keywords : Interval matrix * Spectral decomposition * Matrix power * Eigenvalues * Eigenvectors
OECD category: Pure mathematics
Impact factor: 4.397, year: 2021
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.amc.2021.126174

We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues and eigenvectors of corresponding interval matrices, resulting in the total time complexity O(n^4) where n is the order of the matrix. We present a method for general interval matrices as well as its modification for symmetric interval matrices. In the second part of the paper, we apply the spectral decomposition to computing powers of interval matrices, which is our second goal. Numerical results suggest that a simple binary exponentiation is more efficient for smaller exponents, but our approach becomes better when computing higher powers or powers of a special type of matrices. In particular, we consider symmetric interval and circulant interval matrices. In both cases we utilize some properties of the corresponding classes of matrices to make the power computation more efficient.
Permanent Link: http://hdl.handle.net/11104/0318876