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Properties of Interval Matrices I: Main Results

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

Abstract

In the previous chapters, we analyzed the computational complexity and feasibility of the problems in which the main goal was to compute a number (or an interval). In many practical situations, however, we are not interested in the exact value of this number; all we need to know is whether a certain property is true or not: e.g., whether a given controlled system is stable, etc. It turns out that the most interesting practical problems of this type relate to numerical and interval-values matrices: to check whether a given matrix is regular, positive definite, stable, etc.

In this chapter, we describe the main results related to computational complexity and feasibility of such problems. Proofs and several important auxiliary results are presented in the next chapter.

Keywords

Positive Definiteness Time Time Interval Computation Previous Chapter Interval Matrix 
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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