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A compact algorithm for the intersection and approximation of N-dimensional polytopes

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  • Broman, V.
  • Shensa, M.J.

Abstract

In a very general sense, estimation problems are concerned with relating measurements to a (hopefully small) region containing the unknown state or parameters. Polytopes present a natural candidate for the representation and manipulation of such regions. In fact, assuming the existence of a suitable model, many problems may be reduced to one of efficiently representing N-dimensional polytopes and forming their intersections. The algorithm described in this paper provides a solution to the above problem which is reasonably efficient and requires very little computer code. Although originally developed for use in tracking, it can easily be implemented to perform system identification and has potential application to any problem requiring a versatile representation for N-dimensional convex sets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:469-480
    DOI: 10.1016/0378-4754(90)90003-2
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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