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- W2900397130 abstract "It is well-known that the Chebyshev polynomials $$T_n$$ and $$U_{n-1}$$ can be recursively expressed as linear combinations of $$T_{n-1}$$ and $$U_{n-2}$$ . We study floating-point implementations of these recurrences for arguments in the interval $$[-,1,1]$$ . We demonstrate that the maximum error of the resulting approximation to $$T_n$$ is $$mathcal{O}(un)$$ , where u is the unit roundoff. In contrast, a commonly used three-term recurrence for $$T_n$$ has the maximum error within a constant factor from $$un^2$$ ." @default.
- W2900397130 created "2018-11-16" @default.
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- W2900397130 date "2018-11-09" @default.
- W2900397130 modified "2023-09-24" @default.
- W2900397130 title "Accurate evaluation of Chebyshev polynomials in floating-point arithmetic" @default.
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- W2900397130 doi "https://doi.org/10.1007/s10543-018-0738-5" @default.
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