Direct and iterative methods for interval parametric algebraic systems producing parametric solutions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401025" target="_blank" >RIV/00216208:11320/19:10401025 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jdYoT3-ye4" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jdYoT3-ye4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/nla.2229" target="_blank" >10.1002/nla.2229</a>

Result language
angličtina
Original language name
Direct and iterative methods for interval parametric algebraic systems producing parametric solutions
Original language description
This paper deals with interval parametric linear systems with general dependencies. Motivated by the so-called parameterized solution introduced by Kolev, we consider the enclosures of the solution set in a revised affine form. This form is advantageous to a classical interval solution because it enables us to obtain both outer and inner bounds for the parametric solution set and, thus, intervals containing the endpoints of the hull solution, among others. We propose two solution methods, a direct method called the generalized expansion method and an iterative method based on interval-affine Krawczyk iterations. For the iterative method, we discuss its convergence and show the respective sufficient criterion. For both methods, we perform theoretical and numerical comparisons with some other approaches. The numerical experiments, including also interval parametric linear systems arising in practical problems of structural and electrical engineering, indicate the great usefulness of the proposed methodology and its superiority over most of the existing approaches to solving interval parametric linear systems.
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
—
OECD FORD branch
50201 - Economic Theory

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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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