Evaluation algorithms for multivariate polynomials in Bernstein-Bézier form

DOI10.1016/j.jat.2006.05.007zbMath1104.41007OpenAlexW2016518638MaRDI QIDQ860688

Juan Manuel Peña, Esmeralda Mainar

Publication date: 9 January 2007

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2006.05.007

zbMATH Keywords

multivariate polynomialsde Casteljau algorithmforward errorrunning errorVS algorithm

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

On the accuracy of de Casteljau-type algorithms and Bernstein representations, On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis, Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form, Fast multidimensional Bernstein-Lagrange algorithms, On multivariate polynomials in Bernstein-Bézier form and tensor algebra, A quadratic clipping step with superquadratic convergence for bivariate polynomial systems

Uses Software

• mctoolbox

Cites Work

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• Running error analysis of evaluation algorithms for bivariate polynomials in barycentric Bernstein form
• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
• Efficient evaluation of multivariate polynomials
• Linear convexity conditions for rectangular and triangular Bernstein-Bézier surfaces
• Optimally stable multivariate bases
• Error analysis of corner cutting algorithms
• The evaluation of the zeros of ill-conditioned polynomials. I, II
• Evaluation and approximate evaluation of the multivariate Bernstein-Bézier form on a regularly partitioned simplex
• Monotonicity preservation on triangles
• On the Multivariate Horner Scheme
• Accuracy and Stability of Numerical Algorithms