In this paper a neural network for solving partial differential equations is described. The activation functions of the hidden nodes are the radial basis functions (RBF) whose parameters are learnt by a two-stage gradient descent strategy. A new growing RBF-node insertion strategy with different RBF is used in order to improve the net performances. The learning strategy is able to save computat...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil ...

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon’s smoothing prob...

In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) function...

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equations. In this paper a new approach to the RBF app...

The linear system arised from the interpolation problem of surface divergence-free vector fields using radial basis functions (RBFs) tends to be ill-conditioned when the separation radius of the scattered data is small. When the surface under consideration is the unit sphere, we introduce a preconditioner based on the additive Schwarz method to accelerate the solution process. Theoretical estim...

In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an integral-partial differential equation by using collocation method. For this purpose different applications of RBFs are used. To this end the numerical solutions are obt...

For the problem of low recognition rate on low resolution face images, a super-resolution method for face recognition based on correlated features and nonlinear mappings is proposed in this paper. Canonical correlation analysis (CCA) is applied to establish the correlated subspaces between the features of high and low resolution face images, and radial base functions (RBFs) are employed to cons...

A meshfree radial point interpolation method (RPIM) is developed for stress analysis of threedimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite elemen...