A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems [chapter]

Alexandre Goldsztejn, Gilles Chabert
Numerical Methods and Applications  
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
more » ... d in the context of classical intervals. Some potential applications of this generalized interval LU decomposition are investigated.
doi:10.1007/978-3-540-70942-8_37 dblp:conf/nma/GoldsztejnC06 fatcat:tsnu4qtoc5dpdnmsphfkgn4yn4