On the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind

Alicja Smoktunowicz; Agata Smoktunowicz; Ewa Pawelec

paper

On the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind

arXiv:1312.5677

Abstract

This paper provides error analyses of the algorithms most commonly used for the evaluation of the Chebyshev polynomial of the first kind $T_{N} (x)$ . Some of these algorithms are shown to be backward stable. This means that the computed value of $T_{N} (x)$ in floating point arithmetic by these algorithms can be interpreted as a slightly perturbed value of polynomial $T_{N}$ , for slightly perturbed value of $x$ .