Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
An improved primal simplex variant for pure processing networks
ACM Transactions on Mathematical Software (TOMS)
Implementing the simplex method for the Optimization Subroutine Library
IBM Systems Journal
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
IEEE/ACM Transactions on Networking (TON)
A Status Report on Computing Algorithms for Mathematical Programming
ACM Computing Surveys (CSUR)
A New Steepest Edge Approximation for the Simplex Methodfor Linear Programming
Computational Optimization and Applications
Numerical aspects in developing LP softwares, LPAKO and LPABO
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
A dual method for discrete Chebychev curve fitting
ACM '78 Proceedings of the 1978 annual conference - Volume 2
A Logical Formulation of Probabilistic Spatial Databases
IEEE Transactions on Knowledge and Data Engineering
Maintaining a sparse inverse in the simplex method
IBM Journal of Research and Development
Hi-index | 48.22 |
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.