ADMISSABLE SETS FOR MATRIX EIGENPAIRS


G ALEFELD

goetz.alefeld@mathematik.uni-karlsruhe.de

Institut für Angewandte Mathematik
Universität Karlsruhe
Engkerstaße 2
D-76128 Karlsruhe, Germany



G MAYER

guenter.mayer@mathematik.uni-rostock.de

Fachbereich Mathematik
Universität Rostock
Universitdtsplatz 1
D-18051 Rostock, Germany






Let there be given a real $ (n,n)$ matrix $ A$ which is the center of an interval matrix $ [A- \bigtriangleup A, A+ \bigtriangleup A]=
\ :[A].$ We consider the eigenpair sets

$\displaystyle E=\{(x, \lambda )\in\mathbb{R}^ {n+1} \ \vert \ Ax=\lambda x, A\in[A]\}\\
$

and

       $ E_{\cal P}=\{(x, \lambda )\in\mathbb{R}^{n+1}\ \vert \ Ax=\lambda x, A\in[A], A$ has some property $ \cal P \}$,

respectively. We discuss several equivalent conditions for a pair $ (x, \lambda )$ to belong to $ E$ or to $ E_{\cal P}$, respectively.


EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts