Error bounds for the numerical evaluation of Legendre polynomials by a three-term recurrence

We study the numerical evaluation of the Legendre polynomials [P.sub.n] on the interval [-1, 1] via a three-term recurrence. We prove that in a neighborhood of an endpoint, the computed approximation exactly agrees with the line tangent to [P.sub.n] at this endpoint. As a consequence, we obtain sharp error bounds for the recurrence. Key words. Legendre polynomials, three-term recurrence, floating-point arithmetic AMS subject classifications. 65D20, 65Q30, 33F05