## Experimental Mathematics

### Convergence acceleration of alternating series

#### Abstract

We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $\sum(-1)^ka_k$ with an error of about $17$.$93^{-n}$ from the first $n$ terms for a wide class of sequences $\{a_k\}$. Such methods are useful for high precision calculations frequently appearing in number theory.

#### Article information

Source
Experiment. Math. Volume 9, Issue 1 (2000), 3-12.

Dates
First available in Project Euclid: 5 March 2003

http://projecteuclid.org/euclid.em/1046889587

Mathematical Reviews number (MathSciNet)
MR1758796

Zentralblatt MATH identifier
0972.11115

Subjects
Primary: 11Y55: Calculation of integer sequences
Secondary: 65B05: Extrapolation to the limit, deferred corrections

#### Citation

Cohen, Henri; Rodriguez Villegas, Fernando; Zagier, Don. Convergence acceleration of alternating series. Experiment. Math. 9 (2000), no. 1, 3--12. http://projecteuclid.org/euclid.em/1046889587.