Strong, Strongly Universal and Weak Interval Eigenvectors in Max-Plus Algebra

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18450%2F20%3A50016978" target="_blank" >RIV/62690094:18450/20:50016978 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2227-7390/8/8/1348" target="_blank" >https://www.mdpi.com/2227-7390/8/8/1348</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math8081348" target="_blank" >10.3390/math8081348</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Strong, Strongly Universal and Weak Interval Eigenvectors in Max-Plus Algebra

Popis výsledku v původním jazyce

The scheduling or project management optimization problems, in which the objective function depends on the operations maximum amd plus, can be naturally formulated and solved in max-plus algebra. A system of discrete activations of processors in parallel computing, or activations of some other cooperating machines, is described by a systems of max-plus linear equations. In particular, if the system is in a steady state, such as a synchronized computer network in data processing, then the state vector is an eigenvector of the system. In particular, if the system is in a steady state, such as a synchronized computer network in data processing, then the state vector is an eigenvector of the system. The properties and recognition algorithms for several types of interval eigenvectors are studied in this paper. Then, the strong and the strongly universal eigenvectors are studied and described as max-plus linear combinations of generators. Moreover, a polynomial recognition algorithm is suggested and its correctness is proved. Similar results are presented for the weak eigenvectors. The results are illustrated by numerical examples.

Název v anglickém jazyce

Strong, Strongly Universal and Weak Interval Eigenvectors in Max-Plus Algebra

Popis výsledku anglicky

The scheduling or project management optimization problems, in which the objective function depends on the operations maximum amd plus, can be naturally formulated and solved in max-plus algebra. A system of discrete activations of processors in parallel computing, or activations of some other cooperating machines, is described by a systems of max-plus linear equations. In particular, if the system is in a steady state, such as a synchronized computer network in data processing, then the state vector is an eigenvector of the system. In particular, if the system is in a steady state, such as a synchronized computer network in data processing, then the state vector is an eigenvector of the system. The properties and recognition algorithms for several types of interval eigenvectors are studied in this paper. Then, the strong and the strongly universal eigenvectors are studied and described as max-plus linear combinations of generators. Moreover, a polynomial recognition algorithm is suggested and its correctness is proved. Similar results are presented for the weak eigenvectors. The results are illustrated by numerical examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA18-01246S" target="_blank" >GA18-01246S: Nestandardní optimalizační a rozhodovací metody v manažerských procesech</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

8

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

13

Strana od-do

"Article Number: 1348"

Kód UT WoS článku

000564680600001

EID výsledku v databázi Scopus

2-s2.0-85089960561