Abstract. We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena an...

On page 8 of the paper (page 3209 of the volume), in the seventh line of the second-to-last paragraph of section 5.

Résumé. Nous présentons un algorithme de SVM et des méthodes graphiques pour le traitement de grands ensembles de données. Pour pouvoir traiter de tels ensembles de données, nous utilisons une représentation des données de plus haut niveau (sous forme symbolique). L’algorithme de séparateur à vaste marge (SVM) est adapté pour pouvoir traiter ce nouveau type de données. Nous construisons un nouv...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

The modelling method for creating 3D models in an intuitive way is far from satisfactory. In this paper, we develop a novel mesh fusion method controlled by sketches, which allows users (even novices) to construct complex 3D polygon models fast and easily. The user first cuts needed parts from some existing objects and puts them in right pose. Then, a radial basis function (RBF) based implicit ...

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD)...

In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed me...

Suppose is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal function L (x) = P k2Z c k exp(?(x ? k) 2), x 2 R, satisfying the interpolatory conditions L (j) = 0j , j 2 Z. The paper considers the Gaussian cardinal interpolation operator as a linear mapping from`p (Z) into L p (R), 1 p < 1, and in particular, its behaviour as ! 0 +. It is sh...

For machine learning of an input-output function f from examples, we show it is possible to define an a priori probability density function on the hypothesis space to represent knowledge of the probability distribution of f , even when the hypothesis space H is large (i.e., nonparametric). This allows extension of maximum a posteriori (MAP) estimation methods nonparametric function estimation. ...

A connectionist model made up of a combination of RBF networks is proposed the model decomposes multivalued dependencies into local single valued functions theory and applications are presented