Evaluation of Chebyshev polynomials by a three-term recurrence in floating-point arithmetic

This paper studies an approximation to the Chebyshev polynomial T n computed via a three-term recurrence in floating-point arithmetic. It is shown that close to either endpoint of the interval [ - 1 , 1 ] , the numerical approximation coincides with the line tangent to T n at that endpoint. From this representation new upper and lower error bounds are derived.