Convergence acceleration of alternating series

被引：31
|
作者：
Cohen, H [1 ]
Villegas, FR
Zagier, D
机构：
[1] Univ Bordeaux 1, Lab Algorithm Arthmet & Expt A2X, F-33405 Talence, France
[2] Univ Texas, Dept Math, Austin, TX 78712 USA
[3] Max Planck Inst Math, D-53225 Bonn, Germany
来源：
EXPERIMENTAL MATHEMATICS | 2000年 / 9卷 / 01期
关键词：
convergence acceleration; alternating sum; Chebyshev polynomial;
D O I：
10.1080/10586458.2000.10504632
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Sigma(-1)(k)a(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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页码：3 / 12
页数：10
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