  The circumcentered-reflection method (CRM) has been applied for solving
convex feasibility problems. CRM iterates by computing a circumcenter upon a
composition of reflections with respect to convex sets. Since reflections are
based on exact projections, their computation might be costly. In this regard,
we introduce the circumcentered approximate-reflection method (CARM), whose
reflections rely on outer-approximate projections. The appeal of CARM is that,
in rather general situations, the approximate projections we employ are
available under low computational cost. We derive convergence of CARM and
linear convergence under an error bound condition. We also present successful
theoretical and numerical comparisons of CARM to the original CRM, to the
classical method of alternating projections (MAP) and to a correspondent
outer-approximate version of MAP, referred to as MAAP. Along with our results
and numerical experiments, we present a couple of illustrative examples.
