Accurate evaluation of a polynomial and its derivative in Bernstein form ?
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.
compensated algorithm error-free transformation bernstein polynomial polynomial evaluation derivative evaluation round-off error