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Fast and robust algorithm to compute exact polytope parameter bounds

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  • Mo, S.H.
  • Norton, J.P.

Abstract

When bounds on the parameters of a linear-in-the-parameters model are computed, the exact feasible parameter set defined by the bounds (a polytope) is usually approximated by a simpler shape such as an ellipsoid. However, such simpler bounds may be much looser than the exact bounds. A new algorithm for updating the exact bounds is presented and compared with other recently published methods. Computational results illustrate exact polytope-bound updating by this algorithm from records of realistic length.

Suggested Citation

  • Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    • Handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:481-493
    DOI: 10.1016/0378-4754(90)90004-3
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    References listed on IDEAS

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    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    3. Jan Telgen, 1983. "Identifying Redundant Constraints and Implicit Equalities in Systems of Linear Constraints," Management Science, INFORMS, vol. 29(10), pages 1209-1222, October.
    4. T. H. Matheiss & David S. Rubin, 1980. "A Survey and Comparison of Methods for Finding All Vertices of Convex Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 167-185, May.
    5. T. H. Mattheiss, 1973. "An Algorithm for Determining Irrelevant Constraints and all Vertices in Systems of Linear Inequalities," Operations Research, INFORMS, vol. 21(1), pages 247-260, February.
    6. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
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    Cited by:

    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
    3. Keesman, Karel, 1990. "Membership-set estimation using random scanning and principal component analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 535-543.
    4. Pronzato, Luc & Walter, Eric, 1990. "Experiment design for bounded-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 571-584.
    5. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
    6. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    7. da Silva, Ivan N. & de Arruda, Lucia V.R. & do Amaral, Wagner C., 1999. "A novel approach to robust parameter estimation using neurofuzzy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 251-268.
    8. Piet-Lahanier, Hélène & Veres, Sándor M. & Walter, Eric, 1992. "Comparison of methods for solving sets of linear inequalities in the bounded-error context," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(6), pages 515-524.
    9. Norton, J.P. & Mo, S.H., 1990. "Parameter bounding for time-varying systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 527-534.
    10. Clement, Thierry & Gentil, Sylviane, 1990. "Recursive membership set estimation for output-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 505-513.

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