Relations between various methods for solving linear interval and parametric equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401028" target="_blank" >RIV/00216208:11320/19:10401028 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YgZrqU_VzF" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YgZrqU_VzF</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2019.03.019" target="_blank" >10.1016/j.laa.2019.03.019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relations between various methods for solving linear interval and parametric equations

Popis výsledku v původním jazyce

In the first part of the paper, we consider standard systems of linear interval equations and we focus particularly on two solution methods, the Bauer-Skeel method and the Hansen-Bliek-Rohn method. We show relations between these two methods and between various modifications that are based on preconditioning of the system and on the residual form. We compare as well the quality of the bounds produced by the different variants and we show that for some variants, the Bauer-Skeel bounds naturally arise from other approaches such as Krawczyk of Jacobi iterations, too. In the second part of the paper, we consider interval parametric linear systems with affine-linear dependencies. We also investigate various forms of enclosures, and we not only compare them with each other, but we also show relations to some already known methods. As a consequence, we come up with novel and interesting relations between several algorithms. (C) 2019 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Relations between various methods for solving linear interval and parametric equations

Popis výsledku anglicky

In the first part of the paper, we consider standard systems of linear interval equations and we focus particularly on two solution methods, the Bauer-Skeel method and the Hansen-Bliek-Rohn method. We show relations between these two methods and between various modifications that are based on preconditioning of the system and on the residual form. We compare as well the quality of the bounds produced by the different variants and we show that for some variants, the Bauer-Skeel bounds naturally arise from other approaches such as Krawczyk of Jacobi iterations, too. In the second part of the paper, we consider interval parametric linear systems with affine-linear dependencies. We also investigate various forms of enclosures, and we not only compare them with each other, but we also show relations to some already known methods. As a consequence, we come up with novel and interesting relations between several algorithms. (C) 2019 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

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)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

574

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000468261000001

EID výsledku v databázi Scopus

2-s2.0-85063395758