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Published in:
2007 | OriginalPaper | Chapter
A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems
Authors : Alexandre Goldsztejn, Gilles Chabert
Published in: Numerical Methods and Applications
Publisher: Springer Berlin Heidelberg
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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.