Scattered data interpolation using Radial Basis Functions (RBFs) involves solving ill-conditioned Symmetric Positive Definite (SPD) linear systems; refer e.g. to [6] for further details. We will discuss the properties (conditioning, density) of the interpolation matrices for both global and compactly supported kernels, depending on the value of the shape parameter for both classical global inte...

A general framework for minimal distance methods is presented. Radial Basis Functions (RBFs) and Multilayer Perceptrons (MLPs) neural networks are included in this framework as special cases. New versions of minimal distance methods are formulated. A few of them have been tested on a real-world datasets obtaining very encouraging results.

We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretisation uses Laplace transforms and quadrature. The spatial approximation employs radial basis functions (RBFs) restricted to the sphere. The method allows us to construct high accuracy numerical solutions in parallel.

In this paper, numerical solution of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is obtained by using the mesh-free method based on the collocation method with radial basis functions (RBFs). Stability analysis of the method is discussed. The method is applied to several examples and accuracy of the method is tested in terms of $L_2$ and $L_infty$ error norms.

Search algorithms that use space linear in the search depth are widely employed in practice to solve difficult problems optimally, such as planning and scheduling. In this paper, we study the average-case performance of linear-space search algorithms, including depth-first branch-andbound (DFBnB), iterative-deepening (ID), and recursive best-first search (RBFS). To facilitate our analyses, we u...

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...

In this paper, we present a numerical scheme based on collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is generalized version of the arising from form biomolecular modeling case. Applying radial basis functions (RBFs) allows us deal with difficulties complexity domain. To indicate accuracy RBF method, results for two-dimensional models, also stu...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric Gaussian basis function (RBF) that may be anisotropicall...

Quality of physically-based simulation mostly relies upon qualities of the geometrical model of the entities involved. Particularly, Lagrangian formalism (which we focus on since several years) claims for continuous and smooth descriptors. Our current project aims a precise Lagrangian knee kinematics model. The studied knee model has been chosen as built up from actual bones geometries and liga...