We propose a method of function approximation by radial basis function networks. We will demonstrate that this approximation method can be improved by a pre-treatment of data based on a linear model. This approximation method will be applied to option pricing. This choice justifies itself through the known nonlinear nature of the behavior of options price and through the effective contribution ...

Fuzzy control systems have been extensively used on industrial applications. In the recent years Fuzzy Modeling had become the center of attention for researchers in the area. The theory has been oriented mainly to static function approximation and classiication problems but very few publications have addressed the problem of dynamic function approximation. The problem of identiication using no...

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

Multivariate iterative procedures, based on the use of multivariate rational Hermite interpolants, are introduced for the solution of systems of nonlinear equations. To this end, the most recent iteration points are used as interpolation points. Coalescent interpolation points are obtained by repeating the same iteration point a number of times. This new type of iterative procedure can be compl...

We study the approximation of a continuous function field over a compact set T , by a continuous field of ridge approximants over T , named ridge function fields. We first give general density results about function fields, and show how they apply to ridge function fields. We next discuss the parametrization of sets of ridge function fields, and give additional density results for some class of...

While it is well-known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies compatible with numerical implementation in they required be numerically stable. A performance, called stable manifold widths, approximating a model class K Bana...