The Beppo-Levi native spaces which arise when using polyharmonic splines to interpolate in many space dimensions are embedded in Hölder-Zygmund spaces. Convergence rates for radial basis function interpolation are inferred in some special cases.

We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.

This paper presents a new approach for the Radial Basis Function (RBF) interpolation of a vector field. Standard approaches for interpolation randomly select points for interpolation. Our approach uses the knowledge of vector field topology and selects points for interpolation according to the critical points location. We presents the results of interpolation errors on a vector field generated ...

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x) = ∑ λjφ(‖x − xj‖) exist uniquely for the multiquadric radial function φ(r) = √ r2 + c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we...

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally, and then the translates should get different scalings that match the local data densi...

We consider interpolation on a nite uniform grid by means of one of the radial basis functions (RBF) (r) = r

For radial basis function interpolation of scattered data in IR d , the approximative reproduction of high-degree polynomials is studied. Results include uniform error bounds and convergence orders on compact sets. x1. Introduction We consider interpolation of real-valued functions f deened on a set IR d ; d 1. These functions are interpolated on a set X := fx 1 ; : : : ; x N X g of N X 1 pairw...

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.