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On the asymptotics of polynomial interpolation to at the Chebyshev nodes

✍ Scribed by Revers, Michael

Book ID
123185268
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
210 KB
Volume
165
Category
Article
ISSN
0021-9045

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For a polynomial p(x) of a degree n, we study its interpolation and evaluation on a set of Chebyshev nodes, x k = cos((2k + 1)~r/(2n + 2)), k = 0,1,... ,n. This is easily reduced to applying discrete Fourier transforms (DFTs) to the auxiliary polynomial q(w) = w'~p(x), where 2x = ~w + (aw) -1, a ---