Many types of radial basis functions (RBFs) are global, in terms of having large magnitude across the entire domain. Yet, in contrast, for example, with expansions in orthogonal polynomials, RBF expansions exhibit a strong property of locality with regard to their coefficients. That is, changing a single data value mainly affects the coefficients of the RBFs which are centered in the immediate ...

We obtain analytical formulas for the computation of integrals (moments) all most common Radial Basis Functions (usually shortened as RBFs) on polygonal regions that may be nonconvex or even multiply connected. With RBFs finite regularity, such Thin-Plate Splines, Wendland functions and Powers, our Matlab codes, based standard linear solvers corresponding moment matching systems, provide cubatu...

The conventional differential quadrature (DQ) method is limited in its application to regular regions by using functional values along a mesh line to approximate derivatives. In this work, we extend the idea of DQ method to a general case. In other words, any spatial derivative is approximated by a linear weighted sum of all the functional values in the whole physical domain. The weighting coef...

A multilevel sparse kernel-based interpolation (MLSKI) method, suitable for moderately high-dimensional function interpolation problems has been recently proposed in [15]. The method uses both level-wise and direction-wise multilevel decomposition of structured or mildly unstructured interpolation data sites in conjunction with the application of kernel-based interpolants with different scaling...

Many types of radial basis functions (RBFs) are global, in terms of having large magnitude across the entire domain. Yet, in contrast, for example, with expansions in orthogonal polynomials, RBF expansions exhibit a strong property of locality with regard to their coefficients. That is, changing a single data value mainly affects the coefficients of the RBFs which are centered in the immediate ...

Positive and conditionally positive deenite functions, especially radial basis functions and similar functions for spheres, tori, and even Riemannian manifolds, are of interest because of the their well-known ability to synthesize a good surface t from scattered data. More recently, positive deenite basis functions have been employed to analyze scattered data. The methods used to do this involv...

Volume rendering with splatting most commonly decomposes a volume dataset into a field of overlapping radial basis function (RBF) kernels, such as Gaussians. The rendering effort is directly related to the number of RBFs in the volume and the degree of RBF overlap in the rasterization phase. Much work has been done that seeks to lower the number of RBFs by replacing a neighborhood of kernels wi...

An estimated 115,000 firearm injuries occur annually in the United States, and approximately 70% are nonfatal (1). Retained bullet fragments (RBFs) are an infrequently reported, but important, cause of lead toxicity; symptoms are often nonspecific and can appear years after suffering a gunshot wound (2,3). Adult blood lead level (BLL) screening is most commonly indicated for monitoring of occup...

Food security, health, decent livelihoods, gender equity, safe working conditions, cultural identity and participation in cultural life are basic human rights that can be achieved at least in part through the food system. But current trends in the US prevent full realization of these economic, social, and cultural rights (ESCR) for residents, farmers, and wageworkers in the food system. Supply ...

We present a multilevel algorithm based on nonsymmetric collocation with compactly supported radial basis functions for the solution of nonlinear partial diierential equations. At the operator level this algorithm can be viewed as a Newton method. Details of the algorithm as well as numerical experiments are discussed. x1. Introduction Radial basis function (RBF) methods have been studied by va...