Perturbation Simulations of Rounding Errors in the Evaluation of Chebyshev Series

Roberto Barrio (GME, Dep. Matemática Aplicada, Centro Politécnico Superior Universidad de Zaragoza, Spain)

Jean-Claude Berges (Dep. DGA/T/TI/MS/MN, CNES, France)

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: Chebyshev polynomials, Rounding errors, perturbation methods, polynomial evaluation

Categories: F.2.1, G.1.0