Experimental Mathematics

Convergence acceleration of alternating series

Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier

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

Permanent link to this document
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

Keywords
Convergence acceleration alternating sum Chebyshev polynomial

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.


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