TY - JOUR U1 - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed) A1 - Titi, Jihad A1 - Garloff, Jürgen T1 - Fast determination of the tensorial and simplicial Bernstein forms of multivariate polynomials and rational functions JF - Reliable Computing Journal N2 - 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 coefficients which are the coefficients of the polynomial with respect to the tensorial or simplicial Bernstein basis. The methods exploit monotonicity properties of the Bernstein coefficients of monomials as well as a recently developed matrix method for the computation of the Bernstein coefficients of a polynomial over a box. KW - Multivariate polynomial KW - Multivariate rational function KW - Bernstein coefficient KW - Tensorial Bernstein form KW - Simplicial Bernstein form Y1 - 2017 UR - http://nbn-resolving.de/urn:nbn:de:bsz:352-0-410198 SN - 1573-1340 SS - 1573-1340 IS - 25 SP - 24 EP - 37 ER -