  During the last few years progress has been made on several fronts making it
possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity
in a more robust and accurate way. This paper is the first in a series where we
plan to analyze CPM in the light of these new results.
  Here we start by testing high-order summation-by-parts operators, penalty
boundaries and contraint-preserving boundary conditions applied to CPM in a
setting that is simple enough to study all the ingredients in great detail:
Einstein's equations in spherical symmetry, describing a black hole coupled to
a massless scalar field. We show that with the techniques described above, the
errors introduced by Cauchy-perturbative matching are very small, and that very
long term and accurate CPM evolutions can be achieved. Our tests include the
accretion and ring-down phase of a Schwarzschild black hole with CPM, where we
find that the discrete evolution introduces, with a low spatial resolution of
\Delta r = M/10, an error of 0.3% after an evolution time of 1,000,000 M. For a
black hole of solar mass, this corresponds to approximately 5 s, and is
therefore at the lower end of timescales discussed e.g. in the collapsar model
of gamma-ray burst engines.
  (abridged)
