Many practical applications require the reconstruction of a multivariate function from
discrete, unstructured data. This book gives a self-contained, complete introduction into this …

Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a
bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev …

This paper gives a recent overview on numerical aspects of multivariate interpolation and
approximation by radial basis functions. It comments on the correct choice of the basis …

Error estimates for scattered-data interpolation via radial basis functions (RBFs) for target
functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a …

This work investigates the prediction performance of the kriging predictors. We derive some
error bounds for the prediction error in terms of non-asymptotic probability under the uniform …

We analyze the approximation properties of some meshless methods. Three types of
functions systems are discussed: systems of functions that reproduce polynomials, a class of …

Error estimates for scattered data interpolation by “shifts” of a conditionally positive definite
function (CPD) for target functions in its native space, which is its associated reproducing …

Error estimates for scattered data interpolation by “shifts” of a positive definite function for
target functions in the associated reproducing kernel Hilbert space (RKHS) have been …

Radial basis functions (RBFs) are probably best known for their applications to scattered
data problems. Until the 1990s, RBF theory only involved functions that were scalar-valued …