(untitled) (European Journal of Pure and Applied Mathematics, 2025)
We provide a different and detalied proof of the weak convergence of the acyclic Douglas–Rachford iteration to a point whose nearest-point projections onto each of N convex sets coincide. The analysis shows that the cyclic Douglas–Rachford operator is asymptotically regular, its fixed point set matches the intersection of the individual fixed point sets when nonempty, and the iteration converges weakly to such a point. Special cases reveal when the method coincides with alternating projections and when it diverges from von Neumann’s scheme.