Convergence acceleration of alternating series
Cohen, Henri ; Rodriguez Villegas, Fernando ; Zagier, Don
Experiment. Math., Tome 9 (2000) no. 3, p. 3-12 / Harvested from Project Euclid
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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.
Publié le : 2000-05-14
Classification:  Convergence acceleration,  alternating sum,  Chebyshev polynomial,  11Y55,  65B05 
@article{1046889587,
     author = {Cohen, Henri and Rodriguez Villegas, Fernando and Zagier, Don},
     title = {Convergence acceleration of alternating series},
     journal = {Experiment. Math.},
     volume = {9},
     number = {3},
     year = {2000},
     pages = { 3-12},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1046889587}
}

Cohen, Henri; Rodriguez Villegas, Fernando; Zagier, Don. Convergence acceleration of alternating series. Experiment. Math., Tome 9 (2000) no. 3, pp.  3-12. http://gdmltest.u-ga.fr/item/1046889587/