Chen, PengQuarteroni, AlfioRozza, Gianluigi2014-02-242014-02-242014-02-24201410.1051/m2an/2013128https://infoscience.epfl.ch/handle/20.500.14299/101165WOS:000338931500001We 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.empirical interpolation methoda priori convergence analysisKolmogorov N-widthgreedy algorithmreduced basis methodgeometric Brownian motionKarhunen-Loeve expansiontext::journal::journal article::research article