Asymptotic analysis in multivariate worst case approximation with Gaussian kernels

Abstract

We consider a problem of approximation of $d$-variate functions defined on ${\mathbb{R}}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we investigate the growth of the information complexity as $d\to \infty$. The asymptotics are obtained for the case of fixed error threshold and for the case when it goes to zero as $d\to \infty$.