Some results of convergence acceleration for a general ϑ-type algorithm Original Research Article

In this paper, we propose a general ϑ-type algorithm for accelerating the convergence of sequences. It generalizes some known sequence transformations such as the ϑ-algorithm, the iterated ϑ2, the iterated Δ2, and the T-algorithm. Some general convergence acceleration results are given. Some results of practical importance in applications are obtained. Theoretical results are illustrated by numerical examples.