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This paper introduces a generalization of the empirical interpolation method(EIM) and the reduced basis method (RBM) in order to allow their combinationwith data mining and data assimilation. The purpose is to be able to derivesound information from data and reconstruct information, possibly taking intoaccount noise in the acquisition, that can serve as an input to modelsexpressed by partial differential equations. The approach combines dataacquisition (with noise) with domain decomposition techniques and reduced basisapproximations.

A Generalized Empirical Interpolation Method: application of reduced basis techniques to data assimilation