BIT Numerical Mathematics

, Volume 29, Issue 2, pp 356–360

The practical use of the Euler transformation

Authors

  • R. E. Scraton
    • Department of Mathematics and ComputingSultan Qaboos University
Part II Numerical Mathematics

DOI: 10.1007/BF01952689

Cite this article as:
Scraton, R.E. BIT (1989) 29: 356. doi:10.1007/BF01952689

Abstract

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

65M0540G05

CR Category

G.1.0

Copyright information

© BIT Foundations 1989