  An idealized multigrid algorithm for the computation of propagators of
staggered fermions is investigated.
  Exemplified in four-dimensional $SU(2)$ gauge fields, it is shown that the
idealized algorithm preserves criticality under coarsening.
  The same is not true when the coarse grid operator is defined by the Galerkin
prescription.
  Relaxation times in computations of propagators are small, and critical
slowing is strongly reduced (or eliminated) in the idealized algorithm.
  Unfortunately, this algorithm is not practical for production runs, but the
investigations presented here answer important questions of principle.
