Quadrature Rules for the Fm-Transform Polynomial Components

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Quadrature Rules for the Fm-Transform Polynomial Components
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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