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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 323-332, 2021/04/19
We study the numerical evaluation of the Legendre polynomials $P_n$ onthe interval $[-1,1]$ via a three-term recurrence. We prove that ina neighborhood of an endpoint, the computed approximation exactlyagrees with the line tangent to $P_n$ at this endpoint. As aconsequence, we obtain sharp error bounds for the recurrence.
Keywords: Legendre polynomials, three-term recurrence, floating-point arithmetic