Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385563" target="_blank" >RIV/00216208:11320/18:10385563 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.apnum.2017.12.003" target="_blank" >https://doi.org/10.1016/j.apnum.2017.12.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2017.12.003" target="_blank" >10.1016/j.apnum.2017.12.003</a>

Result language
angličtina
Original language name
Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations
Original language description
We investigate the interval generalized Sylvester matrix equation AXB + CXD = F. We propose a necessary condition for its solutions, and also a sufficient condition for boundedness of the whole solution set. The main effort is performed to develop techniques for computing outer estimations of the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator, reducing significantly computational complexity, compared to the Kronecker product form. We then propose an iterative technique for enclosing the solution set. These approaches are based on spectral decompositions of the midpoints of A, B, C and D and in both of them we suppose that the midpoints of A and C are simultaneously diagonalizable as well as for the midpoints of the matrices B and D. Numerical experiments are given to illustrate the performance of the proposed methods.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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