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Alternating polynomials associated with the Chebyshev extrema nodes

✍ Scribed by L Brutman

Publisher: Elsevier Science
Year: 1988
Tongue: English
Weight: 364 KB
Volume: 53
Category: Article
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90074-3

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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 ---