  The von Neumann-Halperin method of alternating projections converges strongly
to the projection of a given point onto the intersection of finitely many
closed affine subspaces. We propose acceleration schemes making use of two
ideas: Firstly, each projection onto an affine subspace identifies a hyperplane
of codimension 1 containing the intersection, and secondly, it is easy to
project onto a finite intersection of such hyperplanes. We give conditions for
which our accelerations converge strongly. Finally, we perform numerical
experiments to show that these accelerations perform well for a matrix model
updating problem.
