Abstract
Some results on the number of operations, that are needed to update the elimination form of the basis inverse of a linear program and to perform the revised simplex-algorithm, are given for different updating methods.
Zusammenfassung
Es werden einige Resultate über die Anzahl der Operationen, welche nötig sind, um die Eliminationsform der Basisinversen eines linearen Programms neu zu berechnen und den revidierten Simplex-Algorithmus durchzuführen, für verschiedene Methoden der Neuberechnung angeben.
References
Bartels, R. H., Golub, G. H.: The simplex method of linear programming using LU decomposition. Comm. ACM12, 266–268, 275–278 (1969).
Dantzig, G. B.: Linear programming and extensions. Princeton: Princeton Univ. Press 1963.
Forrest, J. J. H., Tomlin, J. A.: Updated triangular factors of the basis to maintain sparsity in the product form simplex method. Math. Progr.2, 263–278 (1972).
Mandl, Chr.: Eine vergleichende Untersuchung verschiedener Algorithmen zur Lösung linearer Optimierungsprobleme, Dissertation Nr. 5288, Eidg. Technische Hochschule Zürich, 1974.
Tewarson, R. P.: Sparse matrices. New York: Academic Press 1973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mandl, C. Number of operations for updating the elimination form of the basis-inverse of the revised simplex-algorithm. Computing 18, 365–366 (1977). https://doi.org/10.1007/BF02244023
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02244023