A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems

  • Alexandre Goldsztejn
  • Gilles Chabert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)


Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a LU decomposition of a generalized interval matrix A: the two computed generalized interval matrices L and U satisfy A = LU with equality instead of the weaker inclusion obtained in the context of classical intervals. Some potential applications of this generalized interval LU decomposition are investigated.


Interval Arithmetic Outer Approximation Classical Interval Interval Matrix Interval Matrice 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alexandre Goldsztejn
    • 1
  • Gilles Chabert
    • 2
  1. 1.University of Central Arkansas, Conway 72035 ArkansasUSA
  2. 2.Projet Coprin, INRIA, 2004 route des Lucioles, 06902 Sophia AntipolisFrance

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