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

We prove new error estimates for a three-term recurrence that is used to compute Legendre polynomials. To this end we derive a bilinear representation of the cross-product of Legendre functions and demonstrate estimates of the cross-product that are needed in the error analysis of the recurrence.

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Bibliographic Details
Published in:IMA journal of numerical analysis 2020-01, Vol.40 (1), p.587-605
Main Authors: Hrycak, Tomasz, Schmutzhard, Sebastian
Format: Article
Language:English
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Description
Summary:We prove new error estimates for a three-term recurrence that is used to compute Legendre polynomials. To this end we derive a bilinear representation of the cross-product of Legendre functions and demonstrate estimates of the cross-product that are needed in the error analysis of the recurrence.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/dry079