In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

| Radial basis functions are presented as a practical solution to the problem of interpolating incomplete surfaces derived from three-dimensional (3-D) medical graphics. The speciic application considered is the design of cranial implants for the repair of defects, usually holes, in the skull. Radial basis functions impose few restrictions on the geometry of the interpolation centers and are su...

In this paper we propose a Rescaled Localized Radial Basis Functions (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from classic RBF interpolation technique, we introduce a rescaling that recovers the partition of unity combined with a new algorithm to select the support of the basis. The proposed rescaling generates a set of basis functi...

Cranioplasty is a neurosurgical operation for repairing cranial defects that have occurred in a previous operation or trauma. Various methods have been presented for cranioplasty from past to present. In computer-aided design based methods, quality of an implant depends on operator’s talent. In mathematical model based methods, such as curvefitting and various interpolations, healthy parts of a...

What is now known as the Gibbs phenomenon was first observed in the context of truncated Fourier expansions, but other versions of it arise also in situations such as truncated integral transforms and for different interpolation methods. Radial basis functions (RBF) is a modern interpolation technique which includes both splines and trigonometric interpolations as special cases in 1-D, and it g...

Lachance. M.A. and A.J. Schwartz. Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149. We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points. We provide methods for distinguishing the cases and constructing the parabolas.

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than whe...