Compensated de Casteljau algorithm in K times the working precision

Danny Hermes

Applied Mathematics and Computation, 2019, vol. 357, issue C, 57-74

Abstract: 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” (K−1) 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.

Keywords: Polynomial evaluation; Compensated algorithm; Floating-point arithmetic; Bernstein polynomial; Error-free transformation; Round-off error (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:357:y:2019:i:c:p:57-74

DOI: 10.1016/j.amc.2019.03.047

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