The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurat...

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Main Authors: Juan Zhang, Mei Sun, Enran Hou, Zhaoxing Ma
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/6694369
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spelling doaj-6a9657f7b96840c8b28cf3fd0081fe332021-10-04T01:59:21ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/6694369The Quasi-Optimal Radial Basis Function Collocation Method: A Technical NoteJuan Zhang0Mei Sun1Enran Hou2Zhaoxing Ma3School of Computer Science and TechnologySchool of Computer Science and TechnologySchool of Computer Science and TechnologySchool of Information and Control EngineeringThe traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.http://dx.doi.org/10.1155/2021/6694369
collection DOAJ
language English
format Article
sources DOAJ
author Juan Zhang
Mei Sun
Enran Hou
Zhaoxing Ma
spellingShingle Juan Zhang
Mei Sun
Enran Hou
Zhaoxing Ma
The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
Journal of Mathematics
author_facet Juan Zhang
Mei Sun
Enran Hou
Zhaoxing Ma
author_sort Juan Zhang
title The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
title_short The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
title_full The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
title_fullStr The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
title_full_unstemmed The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
title_sort quasi-optimal radial basis function collocation method: a technical note
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.
url http://dx.doi.org/10.1155/2021/6694369
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