Convergence acceleration of alternating series

Authors
Cohen, H Villegas, FR Zagier, D
Citation
H. Cohen et al., Convergence acceleration of alternating series, EXP MATH, 9(1), 2000, pp. 3-12
Citations number
8
Categorie Soggetti
Mathematics
Journal title
EXPERIMENTAL MATHEMATICS
ISSN journal
10586458 → ACNP
Volume
9
Issue
1
Year of publication
2000
Pages
3 - 12
Database
ISI
SICI code
1058-6458(2000)9:1<3:CAOAS>2.0.ZU;2-R
Abstract
We discuss some linear acceleration methods for alternating series which ar e in theory and in practice much better than that of Euler-Van Wijngaarden. One of the algorithms, for instance, allows one to calculate Sigma(-1)(k)a (k) with an error of about 17.93(-n) from the first n terms for a wide clas s of sequences {a(k)}. Such methods are useful for high precision calculati ons frequently appearing in number theory.