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

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arXiv · 1312.5677

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

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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 $x$.

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Alicja Smoktunowicz, Agata Smoktunowicz, Ewa Pawelec. 2013-12-20. On the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind. https://arxiv.org/abs/1312.5677

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