We extend the classical empirical interpolation method [1] 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 [13]. 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.

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

QUARTERONI, ALFIO MARIA;
2013-01-01

Abstract

We extend the classical empirical interpolation method [1] 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 [13]. 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.
2013
empirical interpolation method, a priori convergence analysis, greedy algorithm, Kol- mogorov N-width, geometric Brownian motion, Karhunen-Loève expansion, reduced basis method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/762334
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