Fast determination of the tensorial and simplicial Bernstein forms of multivariate polynomials and rational functions
نویسندگان
چکیده
Tests for speeding up the determination of the Bernstein enclosure of the range of a multivariate polynomial and a rational function over a box and a simplex are presented. In the polynomial case, this enclosure is the interval spanned by the minimum and the maximum of the Bernstein coe cients which are the coe cients of the polynomial with respect to the tensorial or simplicial Bernstein basis. The methods exploit monotonicity properties of the Bernstein coe cients of monomials as well as a recently developed matrix method for the computation of the Bernstein coe cients of a polynomial over a box.
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