Standard computer implementations of Dantzig's simplex method for linear programming are based upon forming the inverse of the basic matrix and updating the inverse after every step of the method. These implementations have bad round-off error properties. This paper gives the theoretical background for an implementation which is based upon the LU decomposition, computed with row interchanges, of the basic matrix. The implementation is slow, but has good round-off error behavior. The implementation appears as CACM Algorithm 350.
The simplex method of linear programming using LU decomposition
The Latest from CACM
Shape the Future of Computing
ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.
Get InvolvedCommunications of the ACM (CACM) is now a fully Open Access publication.
By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.
Learn More
Join the Discussion (0)
Become a Member or Sign In to Post a Comment