Displaying similar documents to “The three-dimensional Gauss algorithm is strongly convergent almost everywhere.”

Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems

Brigitte Vallée (2000)

Journal de théorie des nombres de Bordeaux

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We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory...