A weighted empirical interpolation method: a priori convergence analysis and applications
We extend the classical empirical interpolation method to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work. We apply our method to geometric Brownian motion, exponential Karhunen-Loeve expansion and reduced basis approximation of non-ane stochastic elliptic equations. We demonstrate its improved accuracy and eciency over the empirical interpolation method, as well as sparse grid stochastic collocation method.
05.2013_NEW_PC-AQ-GR.pdf
openaccess
556.71 KB
Adobe PDF
2a9e149298a77d77ea4677bb1ee38c41