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.
Publisher
Association for Computing Machinery (ACM)
Reference4 articles.
1. Numerical Analysis: Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations
2. DANTZIG G.B. Linear Programming and Extensions. Princeton U. Press Princeton N.J. 1963. DANTZIG G.B. Linear Programming and Extensions. Princeton U. Press Princeton N.J. 1963.
3. HADLEY G. Linear Programming. Addison-Wesley Reading Mass. 1962. HADLEY G. Linear Programming. Addison-Wesley Reading Mass. 1962.
4. WILKINSON J. H. Rounding Errors in Algebraic Processes. Prentice-Hall Series in Automatic Computation Englewood Cliffs N.J. 1963. WILKINSON J. H. Rounding Errors in Algebraic Processes. Prentice-Hall Series in Automatic Computation Englewood Cliffs N.J. 1963.
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