  We present a technique for the approximation of a class of Hilbert
space-valued maps which arise within the framework of Model Order Reduction for
parametric partial differential equations, whose solution map has a meromorphic
structure. Our MOR stategy consists in constructing an explicit rational
approximation based on few snapshots of the solution, in an interpolatory
fashion. Under some restrictions on the structure of the original problem, we
describe a priori convergence results for our technique, hereafter called
minimal rational interpolation, which show its ability to identify the main
features (e.g. resonance locations) of the target solution map. We also
investigate some procedures to obtain a posteriori error indicators, which may
be employed to adapt the degree and the sampling points of the minimal rational
interpolant. Finally, some numerical experiments are carried out to confirm the
theoretical results and the effectiveness of our technique.
