Abstract
We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, while not imposing restrictions on the shape parameter or number of points.
Original language | English (US) |
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Pages (from-to) | 750-766 |
Number of pages | 17 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 43 |
Issue number | 2 |
DOIs | |
State | Published - 2005 |
Externally published | Yes |
Keywords
- Convergence
- Gaussian radial basis functions
- Potential theory
- RBF
- Runge phenomenon
- Stability
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics