1 research outputs found
Compensated de Casteljau algorithm in times the working precision
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
times the working precision. Forward error analysis and numerical
experiments illustrate the accuracy of this family of algorithms