  We consider an enhanced version of the well-kwown "Petrov-Galerkin"
projection in Hilbert spaces. The proposed procedure, dubbed "multi-slice"
projector, exploits the fact that the sought solution belongs to the
intersection of several high-dimensional slices. This setup is for example of
interest in model-order reduction where this type of prior may be computed
off-line. In this note, we provide a mathematical characterization of the
performance achievable by the multi-slice projector and compare the latter with
the results holding in the Petrov-Galerkin setup. In particular, we illustrate
the superiority of the multi-slice approach in certain situations.
