Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation
| Author(s) | Driscoll, Tobin A. | |
| Author(s) | Platte, Rodrigo B. | |
| Date Accessioned | 2004-12-21T16:37:10Z | |
| Date Available | 2004-12-21T16:37:10Z | |
| Publication Date | 2004 | |
| 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, without imposing restrictions on the shape parameter or number of points. | en |
| Sponsor | Supported by NSF DMS-0104229 | |
| Extent | 667615 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/205 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2004-01 | |
| Keywords | Gaussian radial basis functions | en |
| Keywords | RBF | en |
| Keywords | potential theory | en |
| Keywords | Runge phenomenon | en |
| Keywords | convergence | en |
| Keywords | stability | en |
| dc.subject.classification | AMS: 65D05, 41A30 | |
| Title | Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation | en |
| Type | Technical Report | en |