This thesis is a theorical and numerical contribution to wavelet transform in image processing and surface computing. Group theory approach, multiresolution approach and lters banc approach of wavelets basis are reviewed. The wavelet transform applications concern image compression, discrete curve representation and surface approximation by radial functions. We begin by reviewing di erent image...

Positive and conditionally positive deenite functions, especially radial basis functions and similar functions for spheres, tori, and even Riemannian manifolds, are of interest because of the their well-known ability to synthesize a good surface t from scattered data. More recently, positive deenite basis functions have been employed to analyze scattered data. The methods used to do this involv...

A generalised multiquadric radial basis function is a function of the form s(x) = ∑N i=1 diφ(|x − ti|), where φ(r) = ( r2 + τ2 )k/2 , x ∈ Rn, and k ∈ Z is odd. The direct evaluation of an N centre generalised multiquadric radial basis function at m points requires O(mN) flops, which is prohibitive when m and N are large. Similar considerations apparently rule out fitting an interpolating N cent...

The standard approach to the solution of the radial basis function interpolation problem has been recognized as an ill-conditioned problem for many years. This is especially true when infinitely smooth basic functions such as multiquadrics or Gaussians are used with extreme values of their associated shape parameters. Various approaches have been described to deal with this phenomenon. These te...

This study makes the first attempt to apply the Kansa method in the solution of the time fractional diffusion equations, in which the MultiQuadrics and thin plate spline serve as the radial basis function. In the discretization formulation, the finite difference scheme and the Kansa method are respectively used to discretize time fractional derivative and spatial derivative terms. The numerical...

The meshless local Petrov–Galerkin (MLPG) method with radial basis functions (RBFs), and the higher order shear and normal deformable plate theory (HOSNDPT) are used to analyze static infinitesimal deformations of thick laminated composite elastic plates under different boundary conditions. Two types of RBFs, namely, multiquadrics (MQ) and thin plate splines (TPS), are employed for constructing...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

in the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both neumann and dirichlet initial boundaryconditions. this method is a combination of collocation method and radial basis functions (rbfs). the operational matrix of derivative for laguerre-gaussians (lg) radial basis functions is used to reduce the problem to a set of algebraic equations...

Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...