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The Cholesky Method for Interval Data G. Alefeld and G. Mayer

Summary: The Cholesky Method for Interval Data
G. Alefeld and G. Mayer
Institutfür Angewandte Mathematik
Universität KarZsruhe
Postfach 6980
, D-76128 Karlsruhe, Germany
Dedicated to U. Kulisch on the occasion oi his 60th birthday
Submitted by Richard A. Brualdi
We apply the well-known Cholesky method to bound the solutions of linear
systems with symmetrie matriees and right-hand sides both of whieh are varying
within given intervals. We derive eriteria to-guarantee the feasibility and the optimal-
ity of the method. Furthermore, we diseuss some general properties.
It is weIl known that the fonnulae of the Gaussian algorithm can be used
to bound the solutions of the linear systems for which the coefficient matrices
and the right-hand sides are varying within given intervals; see [11], or [3] and
[13], where also criteria for the feasibility of this method can be found. A
method which can be used systematically for linear systems with areal
symmetrie and positive definite point matrix is the Cholesky method. Com-


Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe


Collections: Mathematics