On the optimal continued fraction expansion of a quadratic surd

Keith R. Matthews

doi:10.1017/S1446788712000596

On the optimal continued fraction expansion of a quadratic surd

Keith R. Matthews^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the period structure of the optimal continued fraction expansion of a quadratic surd, in terms of the period of its nearest square continued fraction expansion. The analysis results in a faster algorithm for determining the optimal continued fraction expansion of a quadratic surd.

Original language	English
Pages (from-to)	133-156
Number of pages	24
Journal	Journal of the Australian Mathematical Society
Volume	93
Issue number	1-2
DOIs	https://doi.org/10.1017/S1446788712000596
Publication status	Published - Aug 2012

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title = "On the optimal continued fraction expansion of a quadratic surd",

abstract = "We describe the period structure of the optimal continued fraction expansion of a quadratic surd, in terms of the period of its nearest square continued fraction expansion. The analysis results in a faster algorithm for determining the optimal continued fraction expansion of a quadratic surd.",

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KW - nearest square continued fraction

KW - optimal continued fraction

KW - period length

KW - quadratic surd

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On the optimal continued fraction expansion of a quadratic surd

Abstract

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