We give an explicit example for the selection of the shape parameter for a certain univariate radial basis function (RBF) interpolation problem.

In this paper, we propose a brief and general process to compute the eigenvalue of arbitrary waveguides using meshless method based on radial basis functions (MLM-RBF) interpolation. The main idea is that RBF basis functions are used in a point matching method to solve the Helmholtz equation only in Cartesian system. Two kinds of boundary conditions of waveguide problems are also analyzed. To v...

In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in ℝ d . Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scatt...

Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. This thesis employs a recently dev...

In this paper, Radial Basis Function (RBF) method for interpolating two dimensional functions with localized features defined on irregular domain is presented. RBF points located inside the domain and on its boundary are chosen such that they are the image of conformally mapped points on concentric circles on a unit disk. On the disk, a fast RBF solver to compute RBF coefficients developed by K...

The boundary knot method (BKM) is a recent boundary-type radial basis function (RBF) collocation scheme for general PDE’s. Like the method of fundamental solution (MFS), the RBF is employed to approximate the inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the method uses a non-singular general solution instead of a singular fundamental solution to evaluate the homogeneo...

A new learning algorithm called extreme learning machine (ELM) has recently been proposed for single-hidden layer feedforward neural networks (SLFNs) with additive neurons to easily achieve good generalization performance at extremely fast learning speed. ELM randomly chooses the input weights and analytically determines the output weights of SLFNs. It is proved in theory that ELM can be extend...

In this paper we propose a Rescaled Localized Radial Basis Functions (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from classic RBF interpolation technique, we introduce a rescaling that recovers the partition of unity combined with a new algorithm to select the support of the basis. The proposed rescaling generates a set of basis functi...

This paper proposes a new approach to real time economic and emission dispatch by using orthogonal least-squares (OLS) and modified particle swarm optimization (MPSO) algorithms to construct the radial basis function (RBF) network. The objectives considered are fuel cost and NOx/CO2 emissions. The RBF network is composed of input, hidden, and output layers. The OLS algorithm provides a simple a...

This document is an introduction to radial basis function RBF networks a type of arti cial neural network for application to problems of supervised learning e g regression classi cation and time series prediction It is now only available in PostScript an older and now unsupported hyper text ver sion may be available for a while longer The document was rst published in along with a package of Ma...