Direct and iterative methods for interval parametric algebraic systems producing parametric solutions
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Direct and iterative methods for interval parametric algebraic systems producing parametric solutions
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Direct and iterative methods for interval parametric algebraic systems producing parametric solutions
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
50201 - Economic Theory
Návaznosti výsledku
Projekt
<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Numerical Linear Algebra with Applications
ISSN
1070-5325
e-ISSN
—
Svazek periodika
26
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
GB - Spojené království Velké Británie a Severního Irska
Počet stran výsledku
24
Strana od-do
e2229
Kód UT WoS článku
000462879200004
EID výsledku v databázi Scopus
2-s2.0-85060346238