01557nas a2200133   4500008004100000245009400041210006900135260001700204520109300221100001501314700002201329700002101351856005101372       2014                        en  d00aA weighted empirical interpolation method: A priori convergence analysis and applications0 aweighted empirical interpolation method A priori convergence ana  bEDP Sciences3 aWe extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] 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 [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttp://urania.sissa.it/xmlui/handle/1963/35021