Accurate evaluation of a polynomial and its derivative in Bernstein form

Accurate evaluation of a polynomial and its derivative in Bernstein form
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DOI：
10.1016/j.camwa.2010.05.021
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发表时间：
2010-08
期刊：
Comput. Math. Appl.
影响因子：
--
通讯作者：
Hao Jiang;Shengguo Li;Lizhi Cheng;Fang Su
Hao Jiang;Shengguo Li;Lizhi Cheng;Fang Su
中科院分区：
其他
文献类型：
--
作者：
Hao Jiang;Shengguo Li;Lizhi Cheng;Fang Su

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在计算机辅助几何设计中，多项式通常以Bernstein形式表示。本文提出了两种补偿算法来精确计算具有浮点系数的Bernstein型多项式及其导数。其原理是应用无误差变换对传统的De Casteljau算法进行改进。正演误差分析和数值实验验证了算法的准确性。
In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents two compensated algorithms to accurately evaluate a polynomial and its derivative in Bernstein form with floating point coefficients. The principle is to apply error-free transformation to improve traditional de Casteljau algorithm. Forward error analysis and numerical experiments illustrate the accuracy of our algorithms.