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Preprints, Working Papers, ... Year : 2008

Sharp estimates for the main parameters of the Euclid Algorithm

Loïck Lhote

Abstract

We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in par- ticular the distribution of the bit-complexity which involves two main parameters : digit–costs and length of continuants. We perform a “dy- namical analysis” which heavily uses the dynamical system underlying the Euclidean algorithm. Baladi and Vall´ee [2] have recently designed a general framework for “distributional dynamical analysis”, where they have exhibited asymptotic gaussian laws for a large class of digit–costs. However, this family contains neither the bit–complexity cost nor the length of continuants.
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Dates and versions

hal-00210493 , version 1 (21-01-2008)

Identifiers

  • HAL Id : hal-00210493 , version 1

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Loïck Lhote, Brigitte Vallée. Sharp estimates for the main parameters of the Euclid Algorithm. 2008. ⟨hal-00210493⟩
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