Computing the spectral decomposition of interval matrices and a study on interval matrix powers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00541295" target="_blank" >RIV/67985807:_____/21:00541295 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10435558

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.amc.2021.126174" target="_blank" >http://dx.doi.org/10.1016/j.amc.2021.126174</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.amc.2021.126174" target="_blank" >10.1016/j.amc.2021.126174</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computing the spectral decomposition of interval matrices and a study on interval matrix powers

Popis výsledku v původním jazyce

We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues and eigenvectors of corresponding interval matrices, resulting in the total time complexity O(n^4) where n is the order of the matrix. We present a method for general interval matrices as well as its modification for symmetric interval matrices. In the second part of the paper, we apply the spectral decomposition to computing powers of interval matrices, which is our second goal. Numerical results suggest that a simple binary exponentiation is more efficient for smaller exponents, but our approach becomes better when computing higher powers or powers of a special type of matrices. In particular, we consider symmetric interval and circulant interval matrices. In both cases we utilize some properties of the corresponding classes of matrices to make the power computation more efficient.

Název v anglickém jazyce

Computing the spectral decomposition of interval matrices and a study on interval matrix powers

Popis výsledku anglicky

We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues and eigenvectors of corresponding interval matrices, resulting in the total time complexity O(n^4) where n is the order of the matrix. We present a method for general interval matrices as well as its modification for symmetric interval matrices. In the second part of the paper, we apply the spectral decomposition to computing powers of interval matrices, which is our second goal. Numerical results suggest that a simple binary exponentiation is more efficient for smaller exponents, but our approach becomes better when computing higher powers or powers of a special type of matrices. In particular, we consider symmetric interval and circulant interval matrices. In both cases we utilize some properties of the corresponding classes of matrices to make the power computation more efficient.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics and Computation

ISSN

0096-3003

e-ISSN

1873-5649

Svazek periodika

403

Číslo periodika v rámci svazku

August 2021

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

126174

Kód UT WoS článku

000639134100016

EID výsledku v databázi Scopus

2-s2.0-85103760084