Evaluation algorithms for multivariate polynomials in Bernstein–Bézier form

The evaluation of multivariate polynomials of n variables in Bernstein–Bézier form is considered. A forward error analysis for the corresponding de Casteljau algorithm and the VS algorithm is performed. We also include algorithms that simultaneously evaluate the polynomial and provide “a posteriori” error bounds, without increasing significantly the computational cost. The sharpness of our running error bounds is shown in the case of trivariate polynomials.