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The Empirical Interpolation Method (EIM) is a greedy procedure thatconstructs approximate representations of two-variable functions in separatedform. In its classical presentation, the two variables play a non-symmetricrole. In this work, we give an equivalent definition of the EIM approximation,in which the two variables play symmetric roles. Then, we give a proof for theexistence of this approximation, and extend it up to the convergence of theEIM, and for any norm chosen to compute the error in the greedy step. Finally,we introduce a way to compute a separated representation in the case where thenumber of selected values is different for each variable. In the case of aphysical field measured by sensors, this is useful to discard a broken sensorwhile keeping the information provided by the associated selected field.

Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension