In a radial basis function (RBF) network, the RBF centers and widths can be evolved by a cooperative-competitive genetic algorithm. The set of genetic strings in one generation of the algorithm represents one REP network, not a population of competing networks. This leads to moderate computation times for the algorithm as a whole. Selection operates on individual RBFs rather than on whole netwo...

Compactly supported radial basis functions (RBFs) were used for surface reconstruction of in vivo geometry, translated from two dimensional (2D) medical images. RBFs provide a flexible approach to interpolation and approximation for problems featuring unstructured data in three-dimensional space. Point-set data are obtained from the contour of segmented 2-D slices. Multilevel RBFs allow smoothi...

we introduce a rbfs mesheless method of lines that decomposes the interior and boundary centers to obtain the numerical solution of the time dependent pdes. then, the method is applied with an adaptive algorithm to obtain the numerical solution of one dimensional problem. we show that in the problems in which the solutions contain region with rapid variation, the adaptive rbfs methods are succe...

Cubature formulas (CFs) based on radial basis functions (RBFs) have become an important tool for multivariate numerical integration of scattered data. Although numerous works been published such RBF-CFs, their stability theory can still be considered as underdeveloped. Here, we strive to pave the way towards a more mature RBF-CFs. In particular, prove RBF-CFs compactly supported RBFs under cert...

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...

This paper proposes a Radial Basis Function Neural Network (RBFNN) which reproduces different Radial Basis Functions (RBFs) by means a real parameter q, named q-Gaussian RBFNN. The architecture, weights and node topology are learnt through a Hybrid Algorithm (HA) with the iRprop+ algorithm as the local improvement procedure. In order to test its overall performance, an experimental study with e...

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general solutions of differential operators. In particular, the harmonic Bessel RBF transforms were presented for high-dimensional data processing. It was also found ...

Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data in R. However, a direct evaluation of an n-center RBF expansion at m points requires O(nm) operations, which is prohibitively expensive as n,m increase. We present a new multilevel method for uniformly dense centers and points and d = 1, whose cost is only O(C(n + m)), where C depen...

In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in Driscoll and Heryudono (2007) for adaptive interpolation by radial basis functions (RBFs). More precisely, introduce context methods a maximum profile likelihood estimation (MPLE) criterion optimal selection RBF shape parameter. This choice is completely automatic, provides highly reliable accurate results...

Radial basis function (RBFs) neural networks provide an attractive method for high dimensional nonparametric estimation for use in nonlinear control. They are faster to train than conventional feedforward networks with sigmoidal activation networks (\backpropagation nets"), and provide a model structure better suited for adaptive control. This article gives a brief survey of the use of RBFs and...