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ON THE RADIAL BASIS FUNCTION INTERPOLATION I: SPECTRAL ANALYSIS OF THE INTERPOLATION MATRIX AND THE RELATED OPERATORS
- Authors: Xiao J.1,2,3
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Affiliations:
- China Resources Networks Co., Ltd.
- National University of Singapore
- University of Michigan, Ann Arbor
- Issue: Vol 63, No 5 (2023)
- Pages: 716
- Section: General numerical methods
- URL: https://bakhtiniada.ru/0044-4669/article/view/136126
- DOI: https://doi.org/10.31857/S0044466923050204
- EDN: https://elibrary.ru/DXJOLI
- ID: 136126
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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.
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About the authors
Jianping Xiao
China Resources Networks Co., Ltd.; National University of Singapore; University of Michigan, Ann Arbor
Author for correspondence.
Email: jpxiao0325@gmail.com
China, Shenzhen; Singapore, SITY; USA, Michigan
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