  In this note we describe how to complement the neutrino evolution matrix
calculated at a given energy and trajectory with additional information which
allows to reliably extrapolate it to nearby energies or trajectories without
repeating the full computation. Our method works for arbitrary matter density
profiles, can be applied to any propagation model described by an Hamiltonian,
and exactly guarantees the unitarity of the evolution matrix. As a
straightforward application, we show how to enhance the calculation of the
theoretical predictions for experimentally measured quantities, so that they
remain accurate even in the presence of fast neutrino oscillations.
Furthermore, the ability to "move around" a given energy and trajectory opens
the door to precise interpolation of the oscillation amplitudes within a grid
of tabulated values, with potential benefits for the computation speed of
Monte-Carlo codes. We also provide a set of examples to illustrate the most
prominent features of our approach.
