Error Analysis of Gaussian Interpolation

Question

Is there any theory available on how well I can approximate a function using a basis of Gaussians $$ \phi_k(x) = \exp(-\tfrac{x - x_k}{\lambda_k}) ? $$ I've heard a bit about Gaussian process regression/Kriging, which seems related, but the approach in the related literatur is very statistical and hence not what I am interested in.

Answer 1

Yes, it's called approximation by radial basis functions. See Wendland's Scattered Data Approximation or Fasshauer's Meshfree Approximation Methods With MATLAB.