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.
- URL: http://mathicse.epfl.ch/files/content/sites/mathicse/files/Mathicse%20reports%202013/05.2013_NEW_PC-AQ-GR.pdf
MATHICSE report 05.2013
Record created on 2014-02-24, modified on 2016-08-09