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The Lebesgue Constant for Higher Order Hermite-Fejér Interpolation on the Chebyshev Nodes

✍ Scribed by G.J. Byrne; T.M. Mills; S.J. Smith

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
528 KB
Volume
81
Category
Article
ISSN
0021-9045

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📜 SIMILAR VOLUMES

On Generalized Hermite–Fejér Interpolati
On Generalized Hermite–Fejér Interpolation of Lagrange Type on the Chebyshev Nodes
✍ Graeme J. Byrne; T.M. Mills; Simon J. Smith 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 131 KB

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

On the Positivity of the Fundamental Pol
On the Positivity of the Fundamental Polynomials for Generalized Hermite–Fejér Interpolation on the Chebyshev Nodes
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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