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Reliable Computing

, Volume 13, Issue 4, pp 325–349 | Cite as

Extension of the Hansen-Bliek Method to Right-Quantified Linear Systems

  • Gilles Chabert
  • Alexandre Goldsztejn
Article

Abstract

The problem of finding the smallest box enclosing the united solution set of a linear interval system, also known as the “interval hull” problem, was proven to be NP-hard. However, Hansen, Bliek, and others subsequently, have provided a polynomial-time solution in the case of systems preconditioned by the midpoint inverse matrix.

Based upon a similar approach, this paper deals with the interval hull problem in the context of AE-solution sets, where parameters may be given different quantifiers. A polynomial-time algorithm is proposed for computing the hull of AE-solution sets where parameters involved in the matrix are constrained to be existentially quantified. Such AE-solution sets are called right-quantified solution sets. They have recently been shown to be of practical interest.

Keywords

Candidate Point Support Line Outer Estimation Interval Vector Interval Linear 
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 B.V. 2007

Authors and Affiliations

  1. 1.Projet CoprinINRIASophia AntipolisFrance
  2. 2.University of Central ArkansasConwayUSA

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