Name
Abstract | ||
|---|---|---|
We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces (RKHSs) induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of interpolation with increasingly flat radial basis functions. When the evaluation points are fixed and unisolvent, we show that the worst-case optimal method converges to a polynomial method. In an additional one-dimensional extension, we allow also the points to be selected optimally and show that in this case convergence is to the unique Gaussian-type method that achieves the maximal polynomial degree of exactness. The proofs are based on an explicit characterisation of the Gaussian RKHS in terms of exponentially damped polynomials. |
Year | Venue | DocType |
|---|---|---|
2019 | CoRR | Journal |
Volume | Citations | PageRank |
abs/1906.02096 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karvonen, Toni | 1 | 11 | 6.65 |
| Simo Särkkä | 2 | 0 | 1.35 |