Extension of the Hansen-Bliek Method to Right-Quantified Linear Systems |
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Authors: | Gilles Chabert Alexandre Goldsztejn |
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Affiliation: | (1) Projet Coprin, INRIA, 2004 route des Lucioles, 06902 Sophia Antipolis, France;(2) University of Central Arkansas, Conway, Arkansas, USA |
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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. |
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