JUCS - Journal of Universal Computer Science 4(6): 561-573, doi: 10.3217/jucs-004-06-0561
Perturbation Simulations of Rounding Errors in the Evaluation of Chebyshev Series
expand article infoRoberto Barrio, Jean-Claude Berges§
‡ GME, Dep. Matemática Aplicada, Centro Politécnico Superior Universidad de Zaragoza, Zaragoza, Spain§ Dep. DGA/T/TI/MS/MN, CNES, Toulouse, France
Open Access
This paper presents some numerical simulations of rounding errors produced during evaluation of Chebyshev series. The simulations are based on perturbation theory and use recent software called AQUARELS. They give more precise results than the theoretical bounds (the difference is of some orders of magnitude). The paper concludes by confirming theoretical results on the increment of the error at the end of the interval [-1; 1] and the increased performance achieved by some modifications to Clenshaw's algorithm near those points.
Rounding errors, perturbation methods, Chebyshev polynomials, polynomial evaluation