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An upper bound for the rate of convergence of the Hermite-Fejér process on the extended Chebyshev nodes of the second kind

✍ Scribed by R Bojanic; J Prasad; R.B Saxena

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
351 KB
Volume
26
Category
Article
ISSN
0021-9045

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For f # C [&1, 1], let H m, n ( f, x) denote the (0, 1, ..., m) Hermite Feje r (HF) interpolation polynomial of f based on the Chebyshev nodes. That is, H m, n ( f, x) is the polynomial of least degree which interpolates f (x) and has its first m derivatives vanish at each of the zeros of the nth Ch

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It is shown that the fundamental polynomials for (0, 1, ..., 2m+1) Hermite Feje r interpolation on the zeros of the Chebyshev polynomials of the first kind are nonnegative for &1 x 1, thereby generalising a well-known property of the original Hermite Feje r interpolation method. As an application of