Abstract
The sequence-transformation method due to Vanden Broeck and Schwartz is used to accelerate the convergence of numerical finite-lattice data on ground-state energies to their infinite-lattice limit. Highly accurate estimates of the ground-state energy are obtained for the S=12 antiferromagnetic Heisenberg and XY rings. The ground-state energy of the S=1 antiferromagnetic Heisenberg ring is also estimated accurately.