# Series acceleration

In numerical analysis, series acceleration (sometimes called as convergence improvement[1]) is the name for algorithms that transforms slowly convergent series to rapidly convergent series.[2][3]

## Where it is used

The NSum and NLimit command in Wolfram Mathematica is based on series acceleration.[4] In addition, Romberg integration (a famous numerical integration method) is also based on this technique.[5][6]

• Brezinski, C. (2019). Reminiscences of Peter Wynn, Numerical Algorithms. (Peter Wynn is one of the most famous researchers of series acceleration. This article includes the summary of his studies.)

## Notes

1. Weisstein, Eric W. "Convergence Improvement." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConvergenceImprovement.html
2. N. Osada (1993) Acceleration Methods for Slowly Convergent Sequences and their Applications, PhD Thesis.
3. Brezinski, C., & Redivo-Zaglia, M. (2019). The genesis and early developments of Aitken’s process, Shanks transformation, the ${\displaystyle \epsilon }$ -algorithm, and related fixed point methods. Numerical Algorithms, 80(1), 11-133.
4. Weisstein, Eric W. ”Wynn’s Epsilon Method.” From MathWorld–A Wolfram Web Resource.
5. Romberg, W. (1955). Vereinfachte numerische integration. Norske Vid. Selsk. Forh., 28, 30-36.
6. F. L. Bauer, H. Rutishauser and E. Stiefel, New aspects in numerical quadrature, Proc. Symp. Appl. Math. (AMS, 1963), vol. 15, p. 198–218.