Bartels R.H., Golub G.H. The simplex method of linear programming using LU decomposition // Communications of the ACM. -1969. Vol. 12, No. 5.

Bartels R.H., Golub G.H. The simplex method of linear programming using LU decomposition // Communications of the ACM. -1969. Vol. 12, No. 5. –P. 266-268.

ABSTRACT

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.