The Lebesgue Function for Generalized Hermite-fejer Interpolation on the Chebyshev Nodes
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چکیده
This paper presents a short survey of convergence results and properties of the Lebesgue function kmn(x) for (0, 1 , . . . , m) Hermite-Fejer interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n -*• oo of the Lebesgue constant Amn = max{Xm n(x) : — 1 < x < 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Amn. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of ^•m.nix) if m > 2 is even.
منابع مشابه
On Hermite-fejer Type Interpolation on the Chebyshev Nodes
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