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
Roberto 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
Corresponding author: Roberto Barrio ( rabarrio@posta.unizar.es ) © Roberto Barrio, Jean-Claude Berges. This article is freely available under the J.UCS Open Content License. Citation:
Barrio R, Berges J-C (1998) Perturbation Simulations of Rounding Errors in the Evaluation of Chebyshev Series. JUCS - Journal of Universal Computer Science 4(6): 561-573. https://doi.org/10.3217/jucs-004-06-0561 |  |
Abstract
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.
Keywords
Rounding errors, perturbation methods, Chebyshev polynomials, polynomial evaluation