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Computing the spectral decomposition of interval matrices and a study on interval matrix powers
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SYSNO ASEP 0541295 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Computing the spectral decomposition of interval matrices and a study on interval matrix powers Author(s) Hartman, David (UIVT-O) RID, SAI, ORCID
Hladík, M. (CZ)
Říha, D. (CZ)Number of authors 3 Article number 126174 Source Title Applied Mathematics and Computation. - : Elsevier - ISSN 0096-3003
Roč. 403, August 2021 (2021)Number of pages 13 s. Publication form Print - P Language eng - English Country US - United States Keywords Interval matrix ; Spectral decomposition ; Matrix power ; Eigenvalues ; Eigenvectors OECD category Pure mathematics Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000639134100016 EID SCOPUS 85103760084 DOI 10.1016/j.amc.2021.126174 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022 Electronic address http://dx.doi.org/10.1016/j.amc.2021.126174
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