id: 00012533
dt: j
an: 00012533
au: Kelling, Birgit; Oelschlägel, Dieter
ti: Solution of linear tolerance problems. (Zur Lösung von linearen
    Toleranzproblemen.)
so: Wiss. Z. Tech. Hochsch. Carl Schorlemmer Leuna-Merseburg 33, No.1, 121-131
    (1991).
py: 1991
pu: Technische Hochschule "Carl Schorlemmer" Leuna-Merseburg, Merseburg
la: DE
cc: 
ut: interval analysis; linear tolerance problem; linear interval equations;
    numerical example
ci: 
li: 
ab: Assume that $[A\sb 1,A\sb 2]$ is an interval of matrices in
    ${\bbfR}\sp{m,n}$, $[a\sb 1,a\sb 2]$ is an interval of vectors in
    ${\bbfR}\sp m$, and $F$ is a set-valued mapping from ${\bbfR}\sp n$ to
    the powerset of ${\bbfR}\sp m$ with $F(x)=[A\sb 1,A\sb 2]\cdot x+[a\sb
    1,a\sb 2]$. For a prescribed interval $[c\sb 1,c\sb 2]$ in ${\bbfR}\sp
    m$ define the set $T:=\{x\mid x\in {\bbfR}\sp n, F(x)\subseteq [c\sb
    1,c\sb 2]\}$. This $T$ can be interpreted as the set of admissible
    input vectors for a model $F$ such that the output $F(x)$ stays within
    the tolerance-interval $[c\sb 1,c\sb 2]$. The authors investigate the
    problem of computing an interval $[x\sb 1,x\sb 2]$ in ${\bbfR}\sp n$
    that is contained in $T$. This problem is closely related to linear
    interval equations. It is shown that methods of H. Beeck, A. S. Deif,
    K. U. Jahn, A. Neumayer, and J. Rohn can be used to establish an
    algorithm for computing $[x\sb 1,x\sb 2]$. A numerical example with
    $m=n=2$ illustrates the posed problem and its solution.
rv: H.Fischer (München)