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

We demonstrate a relationship between the singular values of the design matrix and the discrete Fourier transform of the radial function for radial basis function networks. We then show how regularisation leads to high frequency filtering of the network output. In certain circumstances, this allows the network parameters to be chosen a priori to appropriately bias the learning process.

Sliding-mode and proportional-derivative-type motion control with radial basis function neural network based estimators for wheeled vehicles Anugrah K. Pamosoaji a , Pham Thuong Cat b & Keum-Shik Hong a c a School of Mechanical Engineering, Pusan National University, Busan, Korea b Department of Automation Technology, Institute of Information Technology, Hanoi, Vietnam c Department of Cogno-Mec...

This paper presents a new tool for fitting a divergence-free vector field tangent to a two dimensional orientable surface P ∈ R to samples of such a field taken at scattered sites on P . This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the me...

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.

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.

As an internal parameter of ball milling process, grinding concentration (GC) is not able to be measured directly. According to ball mill’s principle, based on radial base function (RBF) network, a soft sensor method is presented to estimate the ball mill’s GC. And a novel grey relation analysis method as a way to determine the secondary variables is proposed. Simulation results demonstrate tha...