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--U_--n_--_-Numer. Math. 48, 391-416 (1986)

Summary: --U_-- n_--_-
Numer. Math. 48, 391-416 (1986)
@ Springer-Verlag 1986
Componentwise Inclusion and Exclusion Sets
for Solutions of Quadratic Equations
in Finite Dimensional Spaces
G. Alefeld*
Institut für Angewandte Mathematik, Universität Karlsnihe, Kaiserstr. 12,D-7500 Karlsruhe,
Federal Republic of Germany
Summary. In this paper we use interval arithmetic tools for the com-
putation of componentwise inclusion and exc1usion sets for solutions of
quadratic equations in finite dimensional spaces. We define a mapping for
which under certain assumptions we can construct an interval vector which
is mapped into itself. Using Brouwer's fixed point theorem we conc1ude the
existence of a solution of the original equation in this interval vector.
Under different assumptions we can construct an interval vector such that
the range of the mapping has no point in common with this interval vector.
This implies that there is no solution in this interval vector. Furthermore


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


Collections: Mathematics