On Dimension-independent Rates of Convergence for Function Approximation with Gaussian Kernels

@article{Fasshauer2012OnDR,
  title={On Dimension-independent Rates of Convergence for Function Approximation with Gaussian Kernels},
  author={Gregory E. Fasshauer and Fred J. Hickernell and Henryk Wozniakowski},
  journal={SIAM J. Numerical Analysis},
  year={2012},
  volume={50},
  pages={247-271}
}
This article studies the problem of approximating functions belonging to a Hilbert space Hd with an isotropic or anisotropic translation invariant (or stationary) reproducing kernel with special attention given to the Gaussian kernel Kd(x, t) = exp ( − d ∑ `=1 γ ` (x` − t`) 2 ) for all x, t ∈ R. The isotropic (or radial) case corresponds to using the same shape parameters for all coordinates, namely γ` = γ > 0 for all `, whereas the anisotropic case corresponds to varying shape parameters… CONTINUE READING
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