Title : Pseudozero Set of Multivariate Polynomials

Author : Stef Graillat (Université de Perpignan Via Domitia, France)

Abstract :

The pseudozero set of a system $P$ of polynomials in $n$ variables
is the subset of $\mathbb{C}^n$ consisting of the union of the zeros of
all polynomial systems $Q$ that are near to $P$ in a suitable sense.
This concept arises naturally in Scientific Computing where data
often have a limited accuracy. When the polynomials of the system
are polynomials with complex coefficients, the pseudozero set has
already been studied. In this paper, we focus on the case where
the polynomials of the system have real coefficients and such
that all the polynomials in all the perturbed polynomial systems
have real coefficients as well. We provide an explicit definition
to compute this pseudozero set. At last, we analyze different methods
to visualize this set.

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|Stef GRAILLAT, (LP2A)                      Tel: + 33 (0) 4 68 66 21 35|
|Université de Perpignan Via Domitia        Fax: + 33 (0) 4 68 66 22 87|
|52, avenue Paul Alduy                                                 |
|F-66860 Perpignan Cedex, France                                       |
|http://gala.univ-perp.fr/~graillat         Stef.Graillat@univ-perp.fr |
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