J Austral Math Soc Ser A 50 pp481--504, 1991.

Optimal Approximation by Continued Fractions

Wieb Bosma and Cor Kraaikamp

(Received 20 October 1989; revised 27 April 1990)

Abstract

Among all possible semiregular continued fraction expansions of an irrational number the one with the best approximation properties, in a well-defined and natural sense, is determined. Some properties of this so called optimal continued fraction expansion are described.

1980 AMS Subject Classification (1985 Revision): 11J70, 11K50

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Authors

Wieb Bosma: Department of Pure Mathematics, University of Sydney, Sydney, NSW 2006, Australia.
Cor Kraaikamp: Fakulteit Wiskunde en Informatika, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.

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