**Application of the Bernstein Enclosure of Polynomial Ranges to the Solution of Parametric Linear Systems**

Univ. of Applied Sciences / HTWG Konstanz and University of Konstanz, Germany

The Bernstein expansion of a multivariate polynomial provides bounds on its range over a box and allows the construction of affine lower bound functions
for this polynomial. The bounds and lower bound functions can be guaranteed also in the presence of rounding errors and data uncertainties.
We present some recent results by which the complexity of the Bernstein expansion in the case of sparse polynomials often can be reduced by some
orders of magnitude. A recent application is the enclosure of the solution set of a linear system, where the coefficients of the system are polynomially
depending on parameters which are varying between given bounds. We report on the integration of our software for constructing the Bernstein enclosure
based on the interval library filib++ into a *Mathematica* package for solving parametric systems via the *MathLink* protocol.
Examples from parametric systems arising in the finite element analysis are presented.