Volume 54, pp. 323-332, 2021.

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

Tomasz Hrycak and Sebastian Schmutzhard

Abstract

We study the numerical evaluation of the Legendre polynomials $P_n$ 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 $P_n$ at this endpoint. As a consequence, we obtain sharp error bounds for the recurrence.

Full Text (PDF) [264 KB], BibTeX , DOI: 10.1553/etna_vol54s323

Key words

Legendre polynomials, three-term recurrence, floating-point arithmetic

AMS subject classifications

65D20, 65Q30, 33F05