The -dimensional Gauss transformation: Strong convergence and Lyapunov exponents.
Hardcastle, D.M., Khanin, K. (2002)
Experimental Mathematics
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Displaying similar documents to “The three-dimensional Gauss algorithm is strongly convergent almost everywhere.”
The -dimensional Gauss transformation: Strong convergence and Lyapunov exponents.
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...
On the invariant measure for Jacobi-Perron algorithm.
Schweiger, F. (1990)
Mathematica Pannonica
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The Jacobi-Perron Algorithm and Pisot numbers
Eugène Dubois, Ahmed Farhane, Roger Paysant-Le Roux (2004)
Acta Arithmetica
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Volume as a measure of approximation for the Jacobi-Perron algorithm.
Schweiger, Fritz (2010)
Integers
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Measuring the problem-relevant information in input
Stefan Dobrev, Rastislav Královič, Dana Pardubská (2009)
RAIRO - Theoretical Informatics and Applications
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We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request,...