The practical use of the Euler transformation
- R. E. Scraton
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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.
- S.-Å. Gustafson:Convergence acceleration on a general class of power series. Computing21 (1978), 53–69.
- S.-Å. Gustafson:Algorithm 38: two computer codes for convergence acceleration. Computing21 (1978), 87–91.
- S.-Å. Gustafson:On the stability of a class of convergence acceleration methods for power series. BIT24 (1984), 510–519.
- R. E. Scraton:A note on the summation of divergent power series. Proc. Camb. Phil. Soc.66 (1969), 109–114.
- P. Wynn:A note on the generalized Euler transformation. Computer J.14 (1971), 437–441.
- The practical use of the Euler transformation
BIT Numerical Mathematics
Volume 29, Issue 2 , pp 356-360
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- Kluwer Academic Publishers
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- R. E. Scraton (1)
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- 1. Department of Mathematics and Computing, Sultan Qaboos University, P.O. Box 32486, Al-Khod, Muscat, Sultanate of Oman