Introduction Conclusions References Tables Figures

Article history: Available online 5 August 2008

Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...

We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretisation uses Laplace transforms and quadrature. The spatial approximation employs radial basis functions (RBFs) restricted to the sphere. The method allows us to construct high accuracy numerical solutions in parallel.

What is now known as the Gibbs phenomenon was first observed in the context of truncated Fourier expansions, but other versions of it arise also in situations such as truncated integral transforms and for different interpolation methods. Radial basis functions (RBF) is a modern interpolation technique which includes both splines and trigonometric interpolations as special cases in 1-D, and it g...

The task of faults localization is discussed in a model-free setting. As a tool for its solution we consider a multiclass pattern recognition problem with a metric in the label space. Then, this problem is approximately solved, providing hints on selecting appropriate RBF nets. It was shown that the approximate solution is the exact one in several important cases. Finally, we propose the algori...

This paper proposes an enhanced RBF network that enhances learning algorithms between input layer and middle layer and between middle layer and output layer individually for improving the efficiency of learning. The proposed network applies ART2 network as the learning structure between input layer and middle layer. And the autotuning method of learning rate and momentum is proposed and applied...

Scatterograms of images of training vectors in the hidden space help to evaluate the quality of neural network mappings and understand internal representations created by the hidden layers. Visualization of these representations leads to interesting conclusions about optimal architectures and training of such networks. The usefulness of visualization techniques is illustrated on parity problems...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. Thus, the number of nodes in the stencils can be relatively large compared to the resulting accuracy. The generalization of mehrstellenverfahren (compact) FD (CFD) formu...