We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness C are presented for n = 2, 3, 4 and even higher order, as well as a variety of non-uniform 6-point schemes with C continuity.

The RKHS-based optimal image interpolation method, presented by Chen and de Figueiredo (1993), is applied to scattered potential field measurements. The RKHS which admits only interpolants consistent with Laplace's equation is defined and its kernel, derived. The algorithm is compared to bicubic spline interpolation, and is found to yield vastly superior results.

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in R with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the radial basis functions goes to zero, i.e., the radial basis functions become increasingly flat.

A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms andwhose eigenfunctions are orthogonal polynomialswith respect to Jacobiweights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy...

Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example. ...

The purpose of this paper is the investigation of strong converse results for Bernstein-Durrmeyer operators and their quasi-interpolants. For lower dimensions we improve known results by Knoop and Zhou [16] and Chen, Ditzian and Ivanov [5] in regard to the constants in their estimates and prove a strong converse theorem of type B for the quasi-interpolants introduced by Berdysheva, Jetter and S...

In this paper we are interested in the approximation of continuous surface texture profiles defined only at discretely obtained points. A continuous representation is required in order to be able to apply filtration methods that assume uniform data spacing to practical data that in general is not uniformly spaced. By reconstructing surface profiles as natural cubic spline interpolants accuratel...

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

A proof of Favard can be restructured using quasi-interpolants of the type discussed in these proceedings [6] and his result strengthened.