  We consider a family of linear systems $A_\mu \alpha=C$ with system matrix
$A_\mu$ depending on a parameter $\mu$ and for simplicity parameter-independent
right-hand side $C$. These linear systems typically result from the
finite-dimensional approximation of a parameter-dependent boundary-value
problem. We derive a procedure based on the Empirical Interpolation Method to
obtain a separated representation of the system matrix in the form
$A_\mu\approx\sum_{m}\beta_m(\mu)A_{\mu_m}$ for some selected values of the
parameter. Such a separated representation is in particular useful in the
Reduced Basis Method. The procedure is called nonintrusive since it only
requires to access the matrices $A_{\mu_m}$. As such, it offers a crucial
advantage over existing approaches that instead derive separated
representations requiring to enter the code at the level of assembly. Numerical
examples illustrate the performance of our new procedure on a simple
one-dimensional boundary-value problem and on three-dimensional acoustic
scattering problems solved by a boundary element method.
