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

Electronic Transactions on Numerical Analysis

article

Tomasz Hrycak¹  Sebastian Schmutzhard¹ 

[1] Acoustics Research Institute, Austrian Academy of Sciences

关键词: Legendre polynomials;    three-term recurrence;    floating-point arithmetic;   

DOI  :  10.1553/etna_vol54s323

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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.

【 授权许可】

Unknown