Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpolation when f is continuous. Then, by deriving the normal derivative of the interpolant and of a m...

Craig’s interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes ...

Interpolation with translates of a basis function is a common process in approximation theory. One starts with a single function (the basis function) and a set of interpolation points. The most elementary form of the interpolant then consists of a linear combination of all translates by interpolation points of the basis function. Frequently , low degree polynomials are added to the interpolant....

| This paper presents a quasi-interpolation method for DIV-CURL vector splines in two dimensions on both innnite and nite domains. The quasi-interpolant is a linear combination of translates of dilates of a basis function. In particular, our discussion focuses on the approximation of a vector-valued function deened on a nite domain for practical application purposes. In such a case, edge functi...

Given scattered data on the real line, Favard [4] constructed an interpolant which depends linearly and locally on the data and whose nth derivative is locally bounded by the nth divided differences of the data times a constant depending only on n. It is shown that the (n − 1)th derivative of Favard’s interpolant can be likewise bounded by divided differences, and that one can bound at best two...

This paper presents an a posteriori residual error estimator for diffusion-convectionreaction problems approximated by some cell centered finite volume methods on isotropic or anisotropic meshes in Rd, d = 2 or 3. For that purpose we built a reconstructed approximation, which is an appropriate interpolant of the finite volume solution. The error is then the difference between the exact solution...

This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent cons...

The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In t...

Smolyak’s sparse grid construction is commonly used in a setting involving quadrature of a function of a multidimensional argument over a product region. However, the method can be applied in a straightforward way to the interpolation problem as well. In this discussion, we outline a procedure that begins with a family of interpolants defined on a family of nested tensor product grids, and demo...