K e y w o r d s E l l i p t i c PDEs, Generalized multiquadries, Different shape parameters. 1. I N T R O D U C T I O N The interest in meshfree methods to solve PDEs has grown considerably in the past 15 years. The two principal reasons are: (1) mesh generation over twoand three-dimensional complicated domains may require weeks or months to produce a well-behaved mesh, and (2) the convergence ...

We establish the functional equivalence of a generalized class of Gaussian radial basis function (RBFs) networks and the full Takagi-Sugeno model (1983) of fuzzy inference. This generalizes an existing result which applies to the standard Gaussian RBF network and a restricted form of the Takagi-Sugeno fuzzy system. The more general framework allows the removal of some of the restrictive conditi...

In this paper, the Partition of Unity (PU) method is performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, we present a new multidimensional data structure which makes use of an integer-based scheme. This approach allows to perform an optimized space-partitioning structure. Moreover, because of its flexibility, it turns out...

In this paper we discuss Sobolev bounds on functions that vanish at scattered points on the n-sphereSn in Rn+1. The Sobolev spaces involved may have fractional as well as integer order.We then apply these results to obtain estimates for continuous and discrete least-squares surface fits via radial basis functions (RBFs). We also address a stabilization or regularization technique known as splin...

The transport process is an important part of the research fluid dynamics, especially when it comes to tracer advection in atmosphere or ocean dynamics. In this paper, a series high-order semi-Lagrangian methods for on sphere are considered. formulated entirely three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate s...

We present a new methodology to approximate trapezoidal fuzzy numbers set by using smoothing radial basis functions (RBFs). The uses different error and similarity indices determine compare the accuracy of approximation given data. For proposed method type are defined, called under tension. computation one these from data is described some convergence results proved. Finally, examples in two-di...

Radial Basis Function (RBF) neural networks o er an attractive equation form for use in model-based control because they can approximate highly nonlinear plants and yet are well suited for linear adaptive control. We show how interpreting RBFs as mixtures of Gaussians allows the application of many statistical tools including the EM algorithm for parameter estimation. The resulting EMRBF models...