Date of Defense
John Petro, Mathematics and Statistics
Thomas Richardson, Mathematics and Statistics
Naveed Sherwani, Computer Science
The Euclidian algorithm, one of the oldest known algorithms in mathematics, finds the greatest common divisor (gcd) of a pair of integers. First described in Euclid's Elements, this algorithm has since been adapted to find the gcd of two polynomials with coefficients taken from a field and to find a linear combination of two integers or of two polynomials which yields their gcd. In this paper we address several questions concerning the problem of finding the gcd of a list of more than two integers. First, is there a best or most efficient way to find the gcd of a list of integers? For instance, can we find the gcd more efficiently by considering the integers two at a time or by considering the entire list at once? Is the efficiency of our algorithm improved if we start with the smallest integer in the list? What value do we most often expect for the gcd of a list of integers; specifically, what is the probability that it be the universal divisor 1? In this paper, we analyze three algorithms to find the gcd of a list of integers. Each algorithm is a simple modification of the classical Euclidean algorithm. For each algorithm, we find a bound for the theoretical worst case and compute experimental estimates of the algorithm's complexity using Maple.
Eroh, Linda, "GCD Algorithms: Analysis and Experimental Evaluation" (1993). Honors Theses. 264.
Honors Thesis-Campus Only