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Non-Interval Uncertainty I: Ellipsoid Uncertainty and its Generalizations

  • Vladik Kreinovich
  • Anatoly Lakeyev
  • Jiří Rohn
  • Patrick Kahl
Part of the Applied Optimization book series (APOP, volume 10)

Abstract

In the previous chapters, we considered the problem of estimating the range of a function f(x1,..., xn) under the assumption that each variable xi, is known to belong to a given interval xi = [x̃i - Δi, x̃i, + Δi]. So far, we have analyzed this problem under the assumption that we do not know of any dependency between the variables xi. Under this assumption, the set of all possible values of \( \vec x \) forms a multi-dimensional interval (box) x1 × ... × xn.

In many practical cases, however, there is a known dependency between the variables xi. For the simplest (quadratic) type of this dependency, the set of all possible values of x⃗ forms an ellipsoid. In this chapter, we analyze the computational complexity and feasibility of data processing under such ellipsoid uncertainty.

Keywords

Linear System Check Consistency Quartic Polynomial Ellipsoid Uncertainty Interval Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Vladik Kreinovich
    • 1
  • Anatoly Lakeyev
    • 2
  • Jiří Rohn
    • 3
  • Patrick Kahl
    • 4
  1. 1.University of Texas at El PasoUSA
  2. 2.Computing CenterRussian Academy of SciencesIrkutskRussia
  3. 3.Charles University and Academy of SciencesPragueCzech Republic
  4. 4.IBMTucsonUSA

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