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Application of Wynn's epsilon algorithm to periodic continued fractions

Published online by Cambridge University Press:  20 January 2009

M. J. Jamieson
M. J. Jamieson
Affiliation:
Department of Computing Science, University of Glasgow, Glasgow, Scotland
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The infinite continued fraction

in which

is periodic with period l and is equal to a quadratic surd if and only if the partial quotients, ak, are integers or rational numbers [1]. We shall also assume that they are positive. The transformation discussed below applies only to pure periodic fractions where n is zero.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 2 , June 1987 , pp. 295 - 299
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

1.Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford 1960).Google Scholar
2.Wynn, P., On a device for computing the em(Sn) transformation, Mathematical Tables and Other Aids to Computation 10 (1956), 91–96.CrossRefGoogle Scholar
3.Brezinski, C., Accéleration de la convergence en analyse numérique (Lecture Notes in Mathematics No. 584, Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
4.Wynn, P., Upon systems of recursions which obtain among thé quotients of the Padé table, Numer. Math. 8 (1966), 264–269.Google Scholar
5.Phillips, G. M., Aitken sequences and Fibonacci numbers, Amer. Math. Monthly 91 (1984), 354–357.CrossRefGoogle Scholar