A new method for accelerating convergence of alternating series

摘要

We describe a new method for accelerating the convergence of scalar sequence. We express the new method as a rational fraction, namely the rational approximant. The effectiveness of the new method is compared with the well established methods namely, the Lubkin transformation, the iterated Aitken Δ2 algorithm, the Levin transformation, the Epsilon algorithm and the Brezinski theta algorithm for approximating the partial sum of a given alternating series. Estimates of the partial sum produced by the new rational approximant method are found to be substantially more accurate than the classical methods.