Radial basis function methods are modern ways to approximate multivariate functions,
especially in the absence of grid data. They have been known, tested and analysed for …

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 …

This textbook is designed for graduate students in mathematics, physics, engineering, and
computer science. Its purpose is to guide the reader in exploring contemporary …

Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

A hierarchical scheme is presented for smoothly interpolating scattered data with radial
basis functions of compact support. A nested sequence of subsets of the data is computed …

The capacity of reproducing kernel Hilbert spaces (RKHS) plays an essential role in the
analysis of learning theory. Covering numbers and packing numbers of balls of these …

Hardy's multiquadric and its related interpolators have been found to be highly efficient for
interpolating continuous, multivariate functions, as well as for the solution of partial …

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 …

This contribution will touch the following topics: Short introduction into the theory of
multivariate interpolation and approximation by nitely many (irregular) translates of a (not …