A Solution to the Extended GCD Problem

An improved method for expressing the greatest common divisor of n numbers as an integer linear combination of the numbers is presented and analyzed, both theoretically and practically. The performance of this algorithm is compared with other methods, indicating substantial improvements in the size of the solution. The results are given in the light of the current knowledge about the complexity of extended gcd computations. Thus, finding optimal sets of multipliers has been proved to be an NP-complete problem. We present a relatively efficient approximation algorithm with excellent performance. This problem is interesting in its own right. Furthermore, it has important applications, for example in computing canonical normal forms of integer matrices.

• Type: Conference
• Year: 1995
• Where: ISSAC
• Authors: Bohdan S. Majewski, George Havas
• Keywords: Efficient Approximation Algorithm, Greatest Common Divisor, Integer Linear Combination, ISSAC 1995, Mathematics