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Optimal approximation by continued fractions

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

Wieb Bosma  and
Cor Kraaikamp
Wieb Bosma
Affiliation:
Department of Pure Mathematics University of SydneySydney, NSW 2006, Australia
Cor Kraaikamp
Affiliation:
Fakulteit Wiskunde en Informatika Universiteit van AmsterdamPlantage Muidergracht 24 1018 TV Amsterdam, The Netherlands
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Abstract

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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.

Keywords

continued fractionsdiophantine approximation

MSC classification

Secondary: 11J70: Continued fractions and generalizations 11K50: Metric theory of continued fractions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 3 , June 1991 , pp. 481 - 504
Copyright
Copyright © Australian Mathematical Society 1991

References

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