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.

引用

页码：3 / 12

页数：10

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