The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Algorithm 237: Greatest common divisor
Communications of the ACM
Algorithm 139: Solutions of the diophantine equation
Communications of the ACM
Parallel algorithms for hermite normal form of an integer matrix
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
A solution to the extended gcd problem
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Critical slicing for software fault localization
ISSTA '96 Proceedings of the 1996 ACM SIGSOFT international symposium on Software testing and analysis
New sufficient optimality conditions for integer programming and their application
Communications of the ACM
Certification of algorithm 386 [A1]
Communications of the ACM
Algorithm 386: Greatest common divisor of n integers and multipliers
Communications of the ACM
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Partitioning and Labeling of Loops by Unimodular Transformations
IEEE Transactions on Parallel and Distributed Systems
Optimized Q-pivot for Exact Linear Solvers
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
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A new version of the Euclidean algorithm for finding the greatest common divisor of n integers ai and multipliers xi such that gcd = x1 a1 + ··· + xn an is presented. The number of arithmetic operations and the number of storage locations are linear in n. A theorem of Lamé that gives a bound for the number of iterations of the Euclidean algorithm for two integers is extended to the case of n integers. An algorithm to construct a minimal set of multipliers is presented. A Fortran program for the algorithm appears as Comm. ACM Algorithm 386.