Open Access
2000 Convergence acceleration of alternating series
Henri Cohen, Fernando Rodriguez Villegas, Don Zagier
Experiment. Math. 9(1): 3-12 (2000).


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.


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Henri Cohen. Fernando Rodriguez Villegas. Don Zagier. "Convergence acceleration of alternating series." Experiment. Math. 9 (1) 3 - 12, 2000.


Published: 2000
First available in Project Euclid: 5 March 2003

zbMATH: 0972.11115
MathSciNet: MR1758796

Primary: 11Y55
Secondary: 65B05

Keywords: alternating sum , Chebyshev polynomial , Convergence acceleration

Rights: Copyright © 2000 A K Peters, Ltd.

Vol.9 • No. 1 • 2000
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