Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified b...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 12; no. 16; p. 2597
Main Authors: Kouibia, Abdelouahed, González, Pedro, Pasadas, Miguel, Mustafa, Bassim, Yakhlef, Hossain Oulad, Omri, Loubna
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2024
Subjects:
Approximation
Bivariate analysis
Datasets
generalized Wendland radial basis functions
interpolation
Partial differential equations
Radial basis function
radial basis functions
smoothing
variational methods
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R2, and a comparison with another work is analyzed.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12162597