Multivariate Fuzzy Transform of Complex-Valued Functions Determined by Monomial Basis

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F17%3AA1801LVH" target="_blank" >RIV/61988987:17610/17:A1801LVH - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00500-017-2658-8" target="_blank" >http://dx.doi.org/10.1007/s00500-017-2658-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-017-2658-8" target="_blank" >10.1007/s00500-017-2658-8</a>

Result language
angličtina
Original language name
Multivariate Fuzzy Transform of Complex-Valued Functions Determined by Monomial Basis
Original language description
In this paper, we introduce the multivariate fuzzy transform of higher degree of complex-valued functions. Apart from the orthogonal bases of multivariate complex polynomials of weighted Hilbert spaces that are derived by the Gram-Schmidt orthogonalization process, which can be problematic and imprecise in certain cases, we propose to compute the multivariate fuzzy transform components using a simple matrix calculus with the help of the monomial bases. By this novel approach, we derive two types of upper bound of the approximation error both of multivariate complex-valued functions and of their partial derivatives (the latter by the multivariate higher degree fuzzy transform). The results are demonstrated on 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
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OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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