Quadrature Rules for the Fm-Transform Polynomial Components

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302HZC" target="_blank" >RIV/61988987:17610/22:A2302HZC - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2075-1680/11/10/501" target="_blank" >https://www.mdpi.com/2075-1680/11/10/501</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/axioms11100501" target="_blank" >10.3390/axioms11100501</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quadrature Rules for the Fm-Transform Polynomial Components

Popis výsledku v původním jazyce

The purpose of this paper is to reduce the complexity of computing the components of the integral $F^m$-transform, $mgeq 0$, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton–Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the $F^m$-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the $F^m$-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the $F^m$-transformation for $0leq mleq 3$. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by examples.

Název v anglickém jazyce

Quadrature Rules for the Fm-Transform Polynomial Components

Popis výsledku anglicky

The purpose of this paper is to reduce the complexity of computing the components of the integral $F^m$-transform, $mgeq 0$, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton–Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the $F^m$-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the $F^m$-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the $F^m$-transformation for $0leq mleq 3$. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by 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/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Axioms

ISSN

2075-1680

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

29

Strana od-do

—

Kód UT WoS článku

000874235600001

EID výsledku v databázi Scopus

2-s2.0-85140405966