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
收藏
页码：3 / 12
页数：10
相关论文
共 50 条
  • [41] Acceleration of the Convergence of Series Containing Mathieu Functions Using Shanks Transformation
    Erricolo, Danilo
    IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, 2003, 2 : 58 - 61
  • [42] ASYMPTOTIC BEHAVIOR OF ECKHOFF'S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION
    A.Barkhudaryan
    R.Barkhudaryan
    A.Poghosyan
    Analysis in Theory and Applications, 2007, (03) : 228 - 242
  • [43] Convergence Acceleration of Alternating Least Squares with a Matrix Polynomial Predictive Model for PARAFAC Decomposition of a Tensor
    Shi, Ming
    Zhang, JianQiu
    Hu, Bo
    Wang, Bin
    Lu, Qiyong
    2017 25TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2017, : 1115 - 1119
  • [44] APPROXIMATION OF MEROMORPHIC FUNCTIONS BY RATIONAL ONES AND THE ACCELERATION OF POWER-SERIES CONVERGENCE
    KRUPKA, ZI
    DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1982, (10): : 23 - 27
  • [45] A new method of convergence acceleration of series expansion for analytic functions in the complex domain
    Murashige, Sunao
    Tanaka, Ken'ichiro
    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2015, 32 (01) : 95 - 117
  • [46] Convergence acceleration of Fourier series by analytical and numerical application of Poisson's formula
    Marshall, SL
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (11): : 2691 - 2704
  • [47] A new method of convergence acceleration of series expansion for analytic functions in the complex domain
    Sunao Murashige
    Ken’ichiro Tanaka
    Japan Journal of Industrial and Applied Mathematics, 2015, 32 : 95 - 117
  • [48] Principle of alternating gradient acceleration
    Xie, M
    ADVANCED ACCELERATOR CONCEPTS, 2001, 569 : 850 - 857
  • [49] An Alternating Series
    Chen, Hongwei
    AMERICAN MATHEMATICAL MONTHLY, 2010, 117 (09): : 837 - 838
  • [50] Convergence acceleration techniques
    Jentschura, UD
    Aksenov, SV
    Mohr, PJ
    Savageau, MA
    Soff, G
    NANOTECH 2003, VOL 2, 2003, : 535 - 537
12345