A weighted empirical interpolation method: a priori convergence analysis and applications (Q2877710)

An extension of the classical empirical interpolation is presented. The extension considers a weighted interpolation method. It is developed in order to approximate nonlinear parametric functions with weighted parameters. An example of such functions are random variables obeying several probability distributions. Before stating their results, the authors present a brief description and review about empirical interpolation and some of its applications. After that, a description of the weighted empirical interpolation is given together with an algorithm to be used in applications. The main result of the work is related to bounds on the error of the weighted empirical interpolation method. The proof of this result is presented as well as the proofs of the auxiliary results needed. A comparison with the classical empirical interpolation method is presented as well. Some examples where the method is applied are also given. Among them are an application to the case of geometric Brownian motion and also the case of a multidimensional parametric function.