On the Convergence and Stability of the Epsilon Algorithm

The epsilon-algorithm is a sequence-to-sequence convergence accelerating transformation. Using the theory of totally monotone sequences, qualitative assertions concerning the nature of the derived sequences are made. Asymptotic estimates for the members of the derived sequences are given for the cases in which the members of the original sequence can asymptotically be represented by means of Newton series or by Dirichlet series. A stability analysis of the epsilon-algorithm is carried out, and a short description of the smoothing effect of this algorithm is provided. (Author)