Accurate evaluation of a polynomial and its derivative in Bernstein form

作者：Jiang, Hao^*; Li, Shengguo; Cheng, Lizhi; Su, Fang

来源：Computers & Mathematics with Applications, 2010, 60(3): 744-755.

DOI：10.1016/j.camwa.2010.05.021

• Bernstein polynomial
• Compensated algorithm
• Polynomial evaluation
• Derivative evaluation
• Error-free transformation
• Round-off error

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.

• 出版日期2010-8
• 单位中国人民解放军国防科学技术大学