Let Aρ denote the set of functions analytic in |z| < ρ but not on |z| ρ 1 < ρ < ∞ . Walsh proved that the difference of the Lagrange polynomial interpolant of f z ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and H...

We describe an algorithm for constructing point sets which admit unique Lagrange and Hermite interpolation from the space S 1 3 (() of C 1 splines of degree 3 deened on a general class of triangulations. The triangulations consist of nested polygons whose vertices are connected by line segments. In particular, we have to determine the dimension of S 1 3 (() which is not known for arbitrary tria...

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...

In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be exp...

The aim of this paper is to introduce and analyze a multivariate interpolation scheme of Hermite-Birkhoff type. We found the interpolation space, the interpolation operator and its dual operator. 2000 Mathematics Subject Classification: 65D32