The paper deals with Div-Curl approximation problem by weighted thin plate splines. The weighted thin plate splines are an extension of the well known thin plate splines and are radial basis functions which allow the approximation and interpolation of a scalar functions from a given scattered data. We show how the weighted thin plate splines may also be used for the approximation and interpolat...

Thin plate splines provide smooth interpolation of the given data in two or more dimensions. These are analogous to cubic splines in one dimension. The main objectives of this report is to provide an implementation of the thin plate spine interpolation of data using various efficient methods and to investigate the possibility of using thin plate splines in adaptive optics. In this report, we co...

2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...

I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with p...

Thin plate splines have been used successfully to model curves and surfaces. A new application is in data mining where they are used to model interaction terms. These interaction splines break the \curse of dimensionality" by reducing the high-dimensional nonparametric regression problem to the determination of a set of interdependent surfaces. However, the determination of the corresponding th...

We consider the problem of data interpolation or smoothing using a thin-plate spline approach. The thin-plate spline formulation involves the linear combination of logarithmic kernels. For problems with large data sets, current methods for evaluating the splines are too slow. Recently, Beatson and Newsam 1] have suggested using a form of multi-pole type technique for the rapid evaluation of thi...

Thin plate splines have been used successfully to model curves and surfaces. A new application is in data mining where they are used to model interaction terms. These interaction splines break the \curse of di-mensionality" by reducing the high-dimensional nonparametric regression problem to the determination of a set of interdependent surfaces. However , the determination of the corresponding ...