Codice | 07/2013 |
Titolo | A Weighted Empirical Interpolation Method: A-priori Convergence Analysis and Applications |
Data | 2013-02-21 |
Autore/i | Chen, P.; Quarteroni, A.; Rozza, G. |
Link | Download full text |
Abstract | We extend the conventional 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-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. Keywords: empirical interpolation method, a priori convergence analysis, greedy algorithm, Kolmogorov N-width, geometric Brownian motion, Karhunen-Loeve expansion, reduced basis method |
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