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Journal of Scientific Computing

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22.03.2017

Optimal Selection of Local Approximants in RBF-PU Interpolation

verfasst von: Roberto Cavoretto, Alessandra De Rossi, Emma Perracchione

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

The partition of unity (PU) method, performed with local radial basis function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good accuracy, the question about how many points we have to consider on each local subdomain, i.e. how large can be the local data sets, needs to be answered. Moreover, it is well-known that also the shape parameter affects the accuracy of the local RBF approximants and, as a consequence, of the PU interpolant. Thus here, both the shape parameter used to fit the local problems and the size of the associated linear systems are supposed to vary among the subdomains. They are selected by minimizing an a priori error estimate. As evident from extensive numerical experiments and applications provided in the paper, the proposed method turns out to be extremely accurate also when data with non-homogeneous density are considered.

Nächster Artikel A Posteriori Error Estimates of Two-Grid Finite Element Methods for Nonlinear Elliptic Problems

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Titel: Optimal Selection of Local Approximants in RBF-PU Interpolation
verfasst von: Roberto Cavoretto
Alessandra De Rossi
Emma Perracchione
Publikationsdatum: 22.03.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0418-7

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