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

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 $x$.