Stability of Kernel–Based Interpolation: examples Stefano De Marchi Department of Computer Science, University of Verona (Italy) Robert Schaback Institut f¨ ur Numerische und Angewandte Mathematik, University of G¨ ottingen (Germany) In this file, we collect all examples we ran in order to illustrate the results proved in [1]. Hence, we invite interested readers to refer to the paper [1] for better understanding the content of this note. Figure 1 shows the values Λ X of the Lebesgue constants for the Sobolev/Matern kernel (r/c) ν K ν (r/c) for ν =1.5 at scale c = 20. In this and other examples for kernels with finite smoothness, one can see that our bounds on the Lebesgue constants are valid, but the experimental Lebesgue constants seem to be uniformly bounded. In all cases, the maximum of the Lebesgue function is attained in the interior of the domain. Things are different for infinitely smooth kernels. Figure 2 shows the behavior for the Gaussian. The maximum of the Lebesgue function is attained near the corners for large scales, while the behavior in the interior is as stable as for kernels with limited smoothness. The Lebesgue constants do not seem to be uniformly bounded. A second series of examples was run on 225 regular points in [-1, 1] 2 for different kernels at different scales using a parameter c as Φ c (x) = Φ(x/c). Figures 3 to 5 show how the scaling of the Gaussian kernel influences the shape of the associated Lagrange basis functions. The limit for large scales is called the flat limit [3] which is a Lagrange basis function of the de Boor/Ron polynomial interpolation [4]. It cannot be expected that such Lagrange basis functions are uniformly bounded. In contrast to this, Figure 6 shows the corresponding Lagrange basis function for the Sobolev/Matern kernel at scale 320. The scales were such that the conditions of the kernel matrices were unfeasible for the double scale. Figure 7 shows the Lebesgue function in the situation of Figure 5, while Figure 8 shows the Sobolev/Matern case in the situation of Figure 6. Figures 9 and 10 show how the same Sobolev kernel behaves on scattered data given in Figure 11. The encircled point is where the Lagrange function is taken for Figure 9. Note that the situation does not change dramatically when scattered data are used. We also checked if the large errors in the corners of the domain in Figure 7 disappeared for 1