On the asymptotic analysis of the Euclidean algorithm
β Scribed by G.H. Norton
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 213 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
β¦ Synopsis
Let N > 2 and 8 > 0. For uniformly distributed integers in the interval I-1, N], the Euclidean algorithm requires an average of 121n2( 1
divisions, where C is Porter's constant.
π SIMILAR VOLUMES
Euclid's algorithm for computing the greatest common divisor of 2 numbers is considered to be the oldest proper algorithm known ([10]). This algorithm can be amplified naturally in various ways. The GCD problem for more than two numbers is interesting in its own right. Thus, we can use Euclid's algo
As early as the 16th century, Simon Jacob, a German reckoning master, noticed that the worst case in computing the greatest common divisor of two numbers by the Euclidean algorithm occurs if these numbers are equimultiples of two consecutive members of the Fibonacci sequence.