Journal of Algorithms
Journal of Computational and Applied Mathematics - Special volume on the occasion of the 65th birthday of Professor C. C. Grosjean
Computational recreations in Mathematica
Computational recreations in Mathematica
An upper bound on the average number of iterations of the LLL algorithm
Theoretical Computer Science - Special issue on number theory, combinatorics and applications to computer science
A course in computational algebraic number theory
A course in computational algebraic number theory
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Continued fraction algorithms, functional operators, and structure constants
Theoretical Computer Science
Algorithms for Computing Signs of 2×2 Determinants: Dynamics and Average-Case Analysis
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
An analysis of the Gaussian algorithm for lattice reduction
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Average Bit-Complexity of Euclidean Algorithms
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The optimal LLL algorithm is still polynomial in fixed dimension
Theoretical Computer Science - Latin American theoretical informatics
Dynamical analysis of a class of Euclidean algorithms
Theoretical Computer Science - Latin American theoretical informatics
Cryptocomputing with rationals
FC'02 Proceedings of the 6th international conference on Financial cryptography
Pseudorandomness of a random kronecker sequence
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Multiple GCDs. probabilistic analysis of the plain algorithm
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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The Gaussian algorithm for lattice reduction in dimension 2 is analysed under its standard version. It is found that, when applied to random inputs in a continuous model, the complexity is constant on average, its probability distribution decays geometrically, and the dynamics are characterized by a conditional invariant measure. The proofs make use of connections between lattice reduction, continued fractions, continuants, and functional operators. Analysis in the discrete model and detailed numerical data are also presented.