Stability of kernel-based interpolation
For radial basis and other kernel functions, the stability of the interpolation problem with respect to the approximation space is studied. That is, no particular bases are prescribed, but the ability of the spaces to provide stable approximations is considered. While first choices for the bases such as the kernels themselves often provide bad results, as has been noted in early applications, it is shown in this paper that this is not a property of the space which can do better. The kernels which are addressed do not include the infinitely smooth ones, such as multiquadrics, where the situation is still worse than in the kernels of limited differentiability. The importance of this approach comes from the popularity of the radial basis function interpolation method and its implementation.
scientific article; zbMATH DE number 5675106
scientific article