scholarly journals Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Mohammad Mehdi Mazarei ◽  
Azim Aminataei
Keyword(s):  
Radial Basis Function ◽  
Numerical Solution ◽  
Condition Number ◽  
Basis Function ◽  
Elliptic Partial Differential Equations ◽  
Basis Functions ◽  
Poisson’S Equation ◽  
Radial Basis Function Networks ◽  
Poisson's Equation ◽  
Radial Basis

This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameterr. Further, the condition number which arises in the process is discussed, and a comparison is made between them with our earlier studies and previously known ones. It is shown that the system is stable.

SIDE EFFECTS OF NORMALISING RADIAL BASIS FUNCTION NETWORKS

1996 ◽  
Vol 07 (02) ◽  
pp. 167-179 ◽  
Author(s):  
ROBERT SHORTEN ◽  
RODERICK MURRAY-SMITH
Keyword(s):  
Side Effects ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
Partition Of Unity ◽  
Basis Functions ◽  
Radial Basis Function Networks ◽  
Rbf Network ◽  
Linear Function Approximation ◽  
Radial Basis

Normalisation of the basis function activations in a Radial Basis Function (RBF) network is a common way of achieving the partition of unity often desired for modelling applications. It results in the basis functions covering the whole of the input space to the same degree. However, normalisation of the basis functions can lead to other effects which are sometimes less desirable for modelling applications. This paper describes some side effects of normalisation which fundamentally alter properties of the basis functions, e.g. the shape is no longer uniform, maxima of basis functions can be shifted from their centres, and the basis functions are no longer guaranteed to decrease monotonically as distance from their centre increases—in many cases basis functions can ‘reactivate’, i.e. re-appear far from the basis function centre. This paper examines how these phenomena occur, discusses their relevance for non-linear function approximation and examines the effect of normalisation on the network condition number and weights.

Recursive Particle Swarm Optimization Application for the Radial Basis Function Networks Modeling System

2015 ◽  
Vol 713-715 ◽  
pp. 1817-1820
Author(s):  
Ling Liu ◽  
Min Chen ◽  
Hong Yi Guo
Keyword(s):  
Particle Swarm Optimization ◽  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Basis Functions ◽  
Radial Basis Function Networks ◽  
Historical Knowledge ◽  
Swarm Optimization ◽  
Radial Basis

A Recursive Particle Swarm Optimization (RPSO) is proposed to solve dynamic optimization problems where the data is obtained not once but one by one. The position of each particle swarm is updated recursively based on the continuous data and the historical knowledge. The experiment results indicate that RPSO-based radial basis function networks needs fewer radial basis functions and gives more accurate results than traditional PSO in solving dynamic problems.

Indexed Families of Functionals and Gaussian Radial Basis Functions

2003 ◽  
Vol 15 (2) ◽  
pp. 455-468 ◽  
Author(s):  
Irwin W. Sandberg
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Basis Functions ◽  
Inner Product ◽  
Radial Basis Function Networks ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Finite Dimensional ◽  
Radial Basis

We report on results concerning the capabilities of gaussian radial basis function networks in the setting of inner product spaces that need not be finite dimensional. Specifically, we show that important indexed families of functionals can be uniformly approximated, with the approximation uniform also with respect to the index. Applications are described concerning the classification of signals and the synthesis of reconfigurable classifiers.

Sign in / Sign up

Export Citation Format

Share Document