Gaussian Laws for the Main Parameters of the Euclid Algorithms

We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid Algorithms, both on polynomials and on integer numbers. We study in particular the distribution of the bit-complexity which involves two main parameters: digit-costs and length of remainders. We first sho...

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Bibliographic Details
Published in:	Algorithmica Vol. 50; no. 4; pp. 497 - 554
Main Authors:	Lhote, Loïck, Vallée, Brigitte
Format:	Journal Article Conference Proceeding
Language:	English
Published:	New York Springer-Verlag 01.04.2008 Springer
Subjects:	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Mathematics of Computing Theoretical computing Theory of Computation Dynamical analysis of algorithms Tauberian theorems Average-case analysis Transfer operator Perron’s formula Analysis of algorithms Dynamical systems Euclid’s algorithms Distributional analysis Asymptotic Gaussian laws Probabilistic approach Generating function Similarity Euclidean theory Distributional analysis· Dynamical systems Gaussian distribution Perron's formula .Dynamical analysis of algorithms Polynomial method Dynamical system Modeling Euclid's algorithms· Analysis of algorithms· Average-case analysis Bézout idendity Greatest commun divisor Asymptotic approximation Regularity Algorithm analysis Number theory
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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