BIT Numerical Mathematics

, Volume 29, Issue 2, pp 356–360 | Cite as

The practical use of the Euler transformation

  • R. E. Scraton
Part II Numerical Mathematics


The generalised Euler transformation is a powerful transformation of infinite series which can be used, in theory, for the acceleration of convergence and for analytic continuation. When the transformation is applied to a series with rounded coefficients, its behaviour can differ substantially from that predicted theoretically. In general, analytic continuation is impossible in this case. It is still possible, however, to use the transformation for acceleration of convergence, but some changes are necessary in the method of choosing the optimum parameter value.

AMS Categories

65M05 40G05 

CR Category



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S.-Å. Gustafson:Convergence acceleration on a general class of power series. Computing21 (1978), 53–69.Google Scholar
  2. [2]
    S.-Å. Gustafson:Algorithm 38: two computer codes for convergence acceleration. Computing21 (1978), 87–91.Google Scholar
  3. [3]
    S.-Å. Gustafson:On the stability of a class of convergence acceleration methods for power series. BIT24 (1984), 510–519.Google Scholar
  4. [4]
    R. E. Scraton:A note on the summation of divergent power series. Proc. Camb. Phil. Soc.66 (1969), 109–114.Google Scholar
  5. [5]
    P. Wynn:A note on the generalized Euler transformation. Computer J.14 (1971), 437–441.Google Scholar

Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • R. E. Scraton
    • 1
  1. 1.Department of Mathematics and ComputingSultan Qaboos UniversityAl-Khod, MuscatSultanate of Oman

Personalised recommendations