The Lebesgue Constant for Higher Order Hermite-Fejér Interpolation on the Chebyshev Nodes
نویسندگان
چکیده
منابع مشابه
The Lebesgue Function for Generalized Hermite-fejer Interpolation on the Chebyshev Nodes
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 ex...
متن کاملOn the Lebesgue constant for Lagrange interpolation on equidistant nodes
Properties of the Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that the Lebesgue function can be formulated both in terms of a hypergeometric function 2F1 and Jacobi polynomials. Moreover an integral expression of the Lebesgue function is also obtained. Finally, the asymptotic behavior of the Lebesgue constant is studied.
متن کاملOn Hermite-fejer Type Interpolation on the Chebyshev Nodes
ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...
متن کاملConvergence of Hermite and Hermite-Fejér Interpolation of Higher Order for Freud Weights
We investigate weighted Lp(0 < p <.) convergence of Hermite and Hermite– Fejér interpolation polynomials of higher order at the zeros of Freud orthogonal polynomials on the real line. Our results cover as special cases Lagrange, Hermite– Fejér and Krylov–Stayermann interpolation polynomials. © 2001 Academic Press
متن کاملHermite and Hermite-Fejér interpolation for Stieltjes polynomials
Let wλ(x) := (1−x2)λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying ∫ 1 −1 wλ(x)P (λ) n (x)E (λ) n+1(x)x dx { = 0, 0 ≤ m < n+ 1, = 0, m = n+ 1. In this paper, we show uniform convergence of the Hermite–Fejér interpolation polynomials Hn+1[·] and H2n+1[·] based on the zeros of the Sti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1995
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1056