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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00541295" target="_blank" >RIV/67985807:_____/21:00541295 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/21:10435558
Result on the web
<a href="http://dx.doi.org/10.1016/j.amc.2021.126174" target="_blank" >http://dx.doi.org/10.1016/j.amc.2021.126174</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2021.126174" target="_blank" >10.1016/j.amc.2021.126174</a>

Result language
angličtina
Original language name
Computing the spectral decomposition of interval matrices and a study on interval matrix powers
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-04735S" target="_blank" >GA18-04735S: Novel approaches for relaxation and approximation techniques in deterministic global optimization</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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