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Basic Problem of Interval Computations for Polynomials of a Fixed Number of Variables

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

Abstract

In the previous chapter, we proved that the problem of computing the range f(x1,..., xn) of a given polynomial f(x1,..., xn) over given intervals x1,..., xn is, in general, computationally intractable (NP-hard). Since this general problem is intractable, it is desirable to look for cases in which it is feasible. In this chapter, we analyze what happens when we restrict the number of variables n. Good news is that in this case, a polynomial-time algorithm is possible. Bad news is that the existing polynomial-time algorithms require too much computation time to be practical.

Keywords

Polynomial Time Rational Number Algebraic Function Exponential Time Computational Step 
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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