Abstract
This note describes a new accuracy test for the Forrest-Tomlin method for updating triangular factors of the basis, based on standard error analysis techniques. This test has proved very useful in practice when the method is applied to digitally unstable models.
Research and reproduction of this report were partially supported by the Office of Naval Research under Contract N00014-75-C-0865; U.S. Atomic Energy Commission Contract AT(04-3)-326 PA#18; and U.S. Army Research Office Contract DAHCO4 74 C 0034.
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References
J.J.H. Forrest and J.A. Tomlin, “Updating triangular factors of the basis in the product form simplex method”, Mathematical Programming 2 (1972) 263–278.
M.A. Saunders, “Numerical stability in large-scale linear programming”, in: F.R. de Hoog and C.L. Jarvis, eds., Error approximation and accuracy (University of Queensland Press, 1973) pp. 144–158.
J.H. Wilkinson, Rounding errors in algebraic processes (Prentice-Hall, Englewood Cliffs, N.J., 1963).
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© 1975 The Mathematical Programming Society
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Tomlin, J.A. (1975). An accuracy test for updating triangular factors. In: Balinski, M.L., Hellerman, E. (eds) Computational Practice in Mathematical Programming. Mathematical Programming Studies, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120717
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DOI: https://doi.org/10.1007/BFb0120717
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