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]

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.)
  1. Weisstein, Eric W. "Convergence Improvement." From MathWorld--A Wolfram Web Resource.
  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  -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.

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