Series acceleration

In numerical analysis, series acceleration (sometimes called as convergence improvementWeisstein, Eric W. "Convergence Improvement." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConvergenceImprovement.html) is the name for algorithms that transforms slowly convergent series to rapidly convergent series.N. Osada (1993) Acceleration Methods for Slowly Convergent Sequences and their Applications, PhD Thesis.Brezinski, C., & Redivo-Zaglia, M. (2019). The genesis and early developments of Aitken’s process, Shanks transformation, the -algorithm, and related fixed point methods. Numerical Algorithms, 80(1), 11-133.
Where it is used
The NSum and NLimit command in Wolfram Mathematica is based on series acceleration.Weisstein, Eric W. ”Wynn’s Epsilon Method.” From MathWorld–A Wolfram Web Resource. In addition, Romberg integration (a famous numerical integration method) is also based on this technique.Romberg, W. (1955). Vereinfachte numerische integration. Norske Vid. Selsk. Forh., 28, 30-36.F. L. Bauer, H. Rutishauser and E. Stiefel, New aspects in numerical quadrature, Proc. Symp. Appl. Math. (AMS, 1963), vol. 15, p. 198–218.
Further reading
 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

Other websites
 Convergence acceleration of series
 GNU Scientific Library, Series Acceleration
 N. Osada (1993) Acceleration Methods for Slowly Convergent Sequences and their Applications, Ph.D. Thesis.

Category:Mathematics
Category:Computer science
Category:Sequences and series