# Convergence acceleration of alternating series

## TL;DR

This paper introduces a new, computationally efficient convergence acceleration method for alternating series, comparable in performance to existing methods like Smith's and Ford's modifications of Levin's and Weniger's transformations.

## Contribution

A novel convergence acceleration technique for alternating series that reduces computational and memory costs while maintaining effectiveness.

## Key findings

- The new method has similar performance to existing methods.
- It offers lower computational and memory costs.
- Numerical examples validate its effectiveness.

## Abstract

We propose a new simple convergence acceleration method for wide range class of convergent alternating series. It has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Numerical examples confirm a similar performance of all of them.