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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.

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

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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