Compensated de Casteljau algorithm in K times the working precision

摘要

In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents a family of compensated algorithms to accurately evaluate a polynomial in Bernstein form with floating point coefficients. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. At each stage of computation, round-off error is passed on to first order errors, then to second order errors, and so on. After the computation has been “filtered” times via this process, the resulting output is as accurate as the de Casteljau algorithm performed in K times the working precision. Forward error analysis and numerical experiments illustrate the accuracy of this family of algorithms.