Extrapolation of sequences using a generalized epsilon-algorithm

Abstract

The problem of estimating the limit f_∞ of a sequence f_n converging as f_n − f_∞ = O(n^−λ) as n → ∞, where λ > 0, is discussed. Using the generalization of the ε-algorithm proposed recently by Vanden Broeck and Schwartz, an acceleration scheme is developed. The method is illustrated on several test sequences and compared to other acceleration procedures.