A new algorithm for Chebyshev minimum-error multiplication of reduced affine forms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10365650" target="_blank" >RIV/00216208:11320/17:10365650 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11075-017-0300-6" target="_blank" >http://dx.doi.org/10.1007/s11075-017-0300-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-017-0300-6" target="_blank" >10.1007/s11075-017-0300-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A new algorithm for Chebyshev minimum-error multiplication of reduced affine forms

Popis výsledku v původním jazyce

Reduced affine arithmetic (RAA) eliminates the main deficiency of the standard affine arithmetic (AA), i.e. a gradual increase of the number of noise symbols, which makes AA inefficient in a long computation chain. To further reduce overestimation in RAA computation, a new algorithm for the Chebyshev minimum-error multiplication of reduced affine forms is proposed. The algorithm yields the minimum Chebyshev-type bounds and works in linear time, which is asymptotically optimal. We also propose a simplified version of the algorithm, which performs better for low dimensional problems. Illustrative examples show that the presented approach significantly improves solutions of many numerical problems, such as the problem of solving parametric interval linear systems or parametric linear programming, and also improves the efficiency of interval global optimisation.

Název v anglickém jazyce

A new algorithm for Chebyshev minimum-error multiplication of reduced affine forms

Popis výsledku anglicky

Reduced affine arithmetic (RAA) eliminates the main deficiency of the standard affine arithmetic (AA), i.e. a gradual increase of the number of noise symbols, which makes AA inefficient in a long computation chain. To further reduce overestimation in RAA computation, a new algorithm for the Chebyshev minimum-error multiplication of reduced affine forms is proposed. The algorithm yields the minimum Chebyshev-type bounds and works in linear time, which is asymptotically optimal. We also propose a simplified version of the algorithm, which performs better for low dimensional problems. Illustrative examples show that the presented approach significantly improves solutions of many numerical problems, such as the problem of solving parametric interval linear systems or parametric linear programming, and also improves the efficiency of interval global optimisation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA13-10660S" target="_blank" >GA13-10660S: Intervalové metody pro optimalizační úlohy</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

76

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

1131-1152

Kód UT WoS článku

000416161700014

EID výsledku v databázi Scopus

—