Efficient approximation of random fields for numerical applications

This article is dedicated to the rapid computation of separable expansions for the approximation of random fields. We consider approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. Especially, we provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace norm. Numerical examples are provided to validate and quantify the presented methods.