On Hermite-Fejér type interpolation on the Chebyshev nodes

On 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...

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...

Multivariate polynomial interpolation on Lissajous-Chebyshev nodes

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

Hermite 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...

Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle