Euclidean algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by
Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case ...
The Euclidean algorithm is guaranteed to terminate. In other words, a pair of the form (n, 0) will eventually be produced. 3 Proof. Fix a and b. Let S be the set of all second coordinates that appear as outputs as we perform the Euclidean algorithm starting with (a, b). For ...
Avoiding breakdown and near-breakdown in Lanczos type algorithms breakdown. Taylor was probably the first to propose a look-ahead strategy in the context of theEuclidean algorithm Lanczos algorithm, see [44, 42]. ... C Brezinski,MR Zaglia,H Sadok - 《Numerical Algorithms》 被引量: 157发表:...
C Gavoille,N Hanusse 被引量: 114发表: 1999年 A polynomial-time algorithm for computing shortest paths of bounded curvature amidst moderate obstacles A polynomial-time algorithm for computing a short- est path of bounded curvature amidst moderate ob- stacles (extended abstract). In SCG '96: Pr...
A run-time diagram also illustrates this linear-time behavior of the implemented ESP algorithm.关键词: Computer Science - Computational Geometry Computer Science - Discrete Mathematics F.2.2 G.2.2 DOI: 10.1007/978-3-540-74272-2_82 年份: 2007 ...
Question: Use the Euclidean algorithm to hand-calculate the greatest common divisors of each of the pairs of integers in 13,14,15?, and 16 . calculate the greatest common divisors of each of the pairs of integers in13,14,15,and16....
However, while I found many implementations of the algorithm in various languages, all of the ones I tried (in Ruby, Python, Java, and Javascript) return inaccurate results! Trying 13 steps with 5 pulses was an easy way to break most of them. Luckily, Toussaint’s source, Björklund, pr...
The ideal C ∈ I is called a Euclidean ideal if there exists a function2010 Mathematics Subject Classif i cation. Primary:11A05, Secondary 11R29.Key words and phrases. Euclidean algorithm for number f i elds, Euclidean ideal class, Ideal classgroup, Hilbert class f i eld.1 ...
An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this ...