  Gaussian kernels can be an efficient and accurate tool for multivariate
interpolation. In practice, high accuracies are often achieved in the flat
limit where the interpolation matrix becomes increasingly ill-conditioned.
Stable evaluation algorithms for isotropic Gaussians (Gaussian radial basis
functions) have been proposed based on a Chebyshev expansion of the Gaussians
by Fornberg, Larsson & Flyer and based on a Mercer expansion with Hermite
polynomials by Fasshauer & McCourt. In this paper, we propose a new
stabilization algorithm for the multivariate interpolation with isotropic or
anisotropic Gaussians derived from the generating function of the Hermite
polynomials. We also derive and analyse a new analytic cut-off criterion for
the generating function expansion that allows to automatically adjust the
number of the stabilizing basis functions.
