This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

Radial basis function interpolation has attracted a lot of interest in recent years. For popular choices, for example thin plate splines, this problem has a variational formulation, i.e. the interpolant minimizes a semi-norm on a certain space of radial functions. This gives rise to a function space, called the native space. Every function in this space has the property that the semi-norm of an...

This paper presents a ModifiedVariational Splines Fitting (MVSF) algorithm for surface reconstruction using thin plate splines on scattered patches or points of originally smooth surfaces. In particular, a more accurate derivation of the discrete equations for the energy corresponding to the thin plate model is introduced. The results obtained on simulated data show that the proposed algorithm ...

Bayesian hierarchical models have been used for smoothing splines, thin-plate splines, and L-splines. In analyzing high dimensional data sets, additive models and backfitting methods are often used. A full Bayesian analysis for such models may include a large number of random effects, many of which are not intuitive, so researchers typically use noninformative improper or nearly improper priors...

There is a well-known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of ...

We show how to obtain esthetically pleasing contour plots using New S and GCVPACK. With these codes, thin plate splines can easily be used to interpolate “exact” data, and to produce smoothly varying contour plots, with none of the jagged corners that plague many other interpolation methods. It is noted that GCVPACK can also be used to interpolate data on the sphere and in Euclidean three space...