On almost-Hermite-Fejér-interpolation: pointwise estimates

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...

Pointwise Gopengauz Estimates for Interpolation

We derive some new pointwise estimates for the error in simultaneous approximation of a function f 2 C q ?1; 1] and its derivatives by a polynomial of interpolation and its respective derivatives. Our estimates incorporate the point-wise modulus of continuity and/or pointwise second modulus of continuity, an improvement in precision over estimates heretofore known. Our new methods of constructi...

Pointwise radial minimization: Hermite interpolation on arbitrary domains

In this paper we propose a new kind of Hermite interpolation on arbitrary domains, matching derivative data of arbitrary order on the boundary. The basic idea stems from an interpretation of mean value interpolation as the pointwise minimization of a radial energy function involving first derivatives of linear polynomials. We generalize this and minimize over derivatives of polynomials of arbit...

Convergence 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

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