Abstract: In this paper, we develop nonpolynomial septic spline functions for obtaining smooth approximations to the numerical solution of fourth-order two point boundary value problems occurring in a plate deflection theory. Direct methods of second, fourth and sixth order are developed. It is shown that the present method gives approximations, which are better than other existing methods. Thr...

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...

Modal strain energy (MSE) method is a widely used approximation approach for parameter calculation of damped composite structures. In this paper, iterative MSE proposed to calculate the loss factor damping structure by considering frequency dependence modulus and viscoelastic materials. The applied free spline, plate constrain plate. results show that: obtains minimum relative errors less than ...

A common motif in the expositions of spline-based methods in statistical smoothing or numerical interpolation is an allusion to mechanical analogies—motivated perhaps by a desire to provide some explanation why the resulting shapes ought to be regarded as “natural”. The univariate case has its Oxford English Dictionary reference to draftsman spline as “a flexible strip of wood or hard rubber us...

In this paper, we propose a novel technique to address motion estimation and tracking. Such technique represents the motion field using a regular grid of thin-plate splines, and the moving objects using an implicit function on the image plane that is a cubic interpolation of a ”level set function” defined on this grid. Optical flow is determined through the deformation of the grid and consequen...

This paper attempts to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical...

Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...