Results 1  10
of
187,899
THE NONEUCLIDEANEUCLIDEAN ALGORITHM
"... Abstract. In this paper we demonstrate how the geometrically motivated algorithm to determine whether a two generator real Möbius group acting on the Poincaré plane is or is not discrete can be interpreted as a nonEuclidean Euclidean algorithm. That is, the algorithm can be viewed as an application ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. In this paper we demonstrate how the geometrically motivated algorithm to determine whether a two generator real Möbius group acting on the Poincaré plane is or is not discrete can be interpreted as a nonEuclidean Euclidean algorithm. That is, the algorithm can be viewed
Analysis of the binary Euclidean algorithm
 Directions and Recent Results in Algorithms and Complexity
, 1976
"... The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the binary algorithm and consider its average case behaviour. In ..."
Abstract

Cited by 34 (2 self)
 Add to MetaCart
The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the binary algorithm and consider its average case behaviour
Euclidean algorithms are Gaussian
, 2003
"... Abstract. We prove a Central Limit Theorem for a general class of costparameters associated to the three standard Euclidean algorithms, with optimal speed of convergence, and error terms for the mean and variance. For the most basic parameter of the algorithms, the number of steps, we go further an ..."
Abstract

Cited by 28 (12 self)
 Add to MetaCart
Abstract. We prove a Central Limit Theorem for a general class of costparameters associated to the three standard Euclidean algorithms, with optimal speed of convergence, and error terms for the mean and variance. For the most basic parameter of the algorithms, the number of steps, we go further
Some applications of the Euclidean algorithm
 Proceedings of the Second International Colloquium on Numerical Analysis
, 1994
"... Abstract A simple algorithm like the Euclidean algorithm that everybody knows as a method to compute the greatest common divisor of two integers, when applied in more general situations may solve some unexpected problems. One can trace the fundaments of this algorithm in applications such as the rec ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract A simple algorithm like the Euclidean algorithm that everybody knows as a method to compute the greatest common divisor of two integers, when applied in more general situations may solve some unexpected problems. One can trace the fundaments of this algorithm in applications
Distributional analyses of Euclidean algorithms
 Proceedings ANALCO04, submitted
, 2004
"... We provide a complete analysis of the standard Euclidean algorithm and two of its “fast ” variants, the nearestinteger and the oddquotient algorithm. For a whole family of costs, including the number of iterations, we show that the distribution of the cost is asymptotically normal, and obtain the ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We provide a complete analysis of the standard Euclidean algorithm and two of its “fast ” variants, the nearestinteger and the oddquotient algorithm. For a whole family of costs, including the number of iterations, we show that the distribution of the cost is asymptotically normal, and obtain
ELEMENTARY PROPERTIES OF THE SUBTRACTIVE EUCLIDEAN ALGORITHM
, 1990
"... In a recent article in this journal, T. Moore [4] used a microcomputer to make a study of the length of the Euclidean algorithm in determining the greatest common divisor of two nonzero integers m9 n. Our intention is to make a similar study of the lengths of the subtractive Euclidean algorithm. Rec ..."
Abstract
 Add to MetaCart
In a recent article in this journal, T. Moore [4] used a microcomputer to make a study of the length of the Euclidean algorithm in determining the greatest common divisor of two nonzero integers m9 n. Our intention is to make a similar study of the lengths of the subtractive Euclidean algorithm
Continued Fractions and the Euclidean Algorithm
"... 2 The continued fraction expansion of a real number.................... 2 ..."
Abstract
 Add to MetaCart
2 The continued fraction expansion of a real number.................... 2
Results 1  10
of
187,899