Some of the meshless radial basis function methods used for the numerical solution of partial diierential equations are reviewed. In particular, the diierences between globally and locally supported methods are discussed, and for locally supported methods the important role of smoothing within a multilevel framework is demonstrated. A possible connection between multigrid nite elements and mult...

A complex valued neural network is a neural network, which consists of complex valued input and/or weights and/or thresh olds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in image and visio...

The aim of this study was to determine the probability of working days (PWD) for tillage operation using weather data with Multiple Linear Regression (MLR) and Radial Basis Function (RBF) artificial networks. In both models, seven variables were considered as input parameters, namely minimum, average and maximum temperature, relative humidity, rainfall, wind speed, and evaporation on a daily ba...

The use of the K-means algorithm and the K-nearest neighbor heuristic in estimating the radial basis function (RBF) parameters may produce sub-optimal performance when the input vectors contain correlated components. This paper proposes to overcome this problem by incorporating full covariance matrices into the RBF structure and to use the expectation-maximi-zation (EM) algorithm to estimate th...

Wavelets and radial basis functions (RBF) are two rather distinct ways of representing signals in terms of shifted basis functions. An essential aspect of RBF, which makes the method applicable to non-uniform grids, is that the basis functions, unlike wavelets, are non-local|in addition, they do not involve any scaling at all. Despite these fundamental di erences, we show that the two types of ...

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD)...

In this paper, we investigate the decision making ability of a fully complex-valued radial basis function (FC-RBF) network in solving real-valued classification problems. The FC-RBF classifier is a single hidden layer fully complex-valued neural network with a nonlinear input layer, a nonlinear hidden layer, and a linear output layer. The neurons in the input layer of the classifier employ the ...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

This paper presents a set of optimizations in learning algorithms commonly used for training radial basis function neural networks. These optimizations are applied to a RBF neural network used in identifying helicopter types processing their rotor sounds. The first method uses an optimum learning rate in each iteration of train process. This method increases the speed of learning process and al...