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

2018 ◽  
Vol 40 (1) ◽  
pp. 587-605
Author(s):  
Tomasz Hrycak ◽  
Sebastian Schmutzhard
Keyword(s):  
Error Analysis ◽  
Error Estimates ◽  
Legendre Polynomials ◽  
Cross Product ◽  
Floating Point ◽  
Legendre Functions ◽  
Floating Point Arithmetic ◽  
The Cross ◽  
Point Arithmetic

Abstract 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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