Efficient evaluation of multivariate polynomials
Computer Aided Geometric Design
Convexity and Bernstein-Be´zier polynomials
Curves and surfaces
ACM Transactions on Mathematical Software (TOMS)
Linear convexity conditions for rectangular and triangular Bernstein-Be´zier surfaces
Computer Aided Geometric Design
On the Multivariate Horner Scheme
SIAM Journal on Numerical Analysis
Montonicity preservation on triangles
Mathematics of Computation
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
Computer Aided Geometric Design
On multivariate polynomials in Bernstein-Bézier form and tensor algebra
Journal of Computational and Applied Mathematics
Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form
Applied Numerical Mathematics
On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
Advances in Computational Mathematics
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The evaluation of multivariate polynomials of n variables in Bernstein-Bezier 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.