On approximate approximations using Gaussian kernels

In Maz'ya (1991), (1994) a new approximation method was proposed mainly directed to the numerical solution of operator equations. This method is characterised by a very accurate approximation in a certain range relevant for numerical computations, but in general the approximations do not converge. For that reason such processes were called approximate approximations (see also Maz'ya and Schmidt (1994)). The present paper is devoted to an application of this method to the approximation of multivariate functions using Gaussian kernels. We study some examples to approximate functions U in Rn by sums of the form