Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form

Authors:
Hao Jiang;Roberto Barrio;Xiangke Liao;Lizhi Cheng
Affiliations:
School of Science, National University of Defense Technology, Changsha, 410073, China;Dpto. de Matemática Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain;School of Computer, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

In this paper it is presented a compensated de Casteljau algorithm to accurately evaluate a bivariate polynomial in Bernstein-Bezier form. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. A forward error and a running error analysis are performed. Finally, some numerical experiments illustrate the accuracy of the proposed algorithm in ill-conditioned problems.