Optimal radial basis for density-based atomic representations

Radial Basis Neural Network Based Islanding Detection in Distributed Generation

This article presents a Radial Basis Neural Network (RBNN) based islanding detection technique. Islanding detection and prevention is a mandatory requirement for grid-connected distributed generation (DG) systems. Several methods based on passive and active detection scheme have been proposed. While passive schemes have a large non detection zone (NDZ), concern has been raised on active method ...

Non local Radial Basis Functions for Forecasting and Density Estimation

AhtractThis paper discusses the rationale for employing alternative basis functions to the ubiquitous Gaussian in Radial Basis Function networks. In particular we concentrate upon employing unbounded basis functions (though the network as a whole remains bounded), and non positive definite basis functions. The use of unbounded and nonpositive basis functions, though counterintuitive in applicat...

Optimal Distribution of Centers for Radial Basis Function Methods

Optimal Approximation Orders in Lp for Radial Basis Functions

We prove that the well known Lp-error estimates for radial basis function interpolation are optimal provided that the underlying function space is the native Hilbert space of the basis function. Furthermore we give upper bounds for the approximation orders in case of best L1-approximation using radial basis functions.

Stable Gaussian radial basis function method for solving Helmholtz equations

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...