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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 5, Page 716
DOI: https://doi.org/10.31857/S0044466923050204 (Mi zvmmf11547) 		 
General numerical methods

On the radial basis function interpolation I: Spectral analysis of the interpolation matrix and the related operators

Jianping Xiaoabc

a China Resources Networks Co., Ltd. Shenzhen, China
b National University of Singapore, SITY, Singapore
c University of Michigan, Ann Arbor, Michigan, USA
DOI: https://doi.org/10.31857/S0044466923050204
Abstract: In this paper, we study the spectral properties of the periodized Radial Basis Function interpolation matrix as well as the related harmonic operators discretized using Radial Basis Functions. For Gaussian RBF, this procedure could be easily extended to an arbitrarily high dimensional space on a tensor-product grid as presented in the later parts of the paper. The experimental result of Boyd’s condition number [1] is analytically well predicted in the context of periodized RBF.
Key words: RBF, interpolation, spectral methods, Neural Network, tensor decomposition.
Funding agency Grant number
National Natural Science Foundation of China
I would like to thank the National Science Foundation for the support of this work.
Received: 11.10.2022
Revised: 11.10.2022
Accepted: 02.02.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 5, Pages 719–729
DOI: https://doi.org/10.1134/S0965542523050172
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: English
Citation: Jianping Xiao, “On the radial basis function interpolation I: Spectral analysis of the interpolation matrix and the related operators”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 716; Comput. Math. Math. Phys., 63:5 (2023), 719–729
Citation in format AMSBIB
\Bibitem{Xia23}
\by Jianping~Xiao
\paper On the radial basis function interpolation I: Spectral analysis of the interpolation matrix and the related operators
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 5
\pages 716
\mathnet{http://mi.mathnet.ru/zvmmf11547}
\crossref{https://doi.org/10.31857/S0044466923050204}
\elib{https://elibrary.ru/item.asp?id=53738564}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 5
\pages 719--729
\crossref{https://doi.org/10.1134/S0965542523050172}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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