Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only non-oscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as their limiting case) leads to non-singular interpolants with in...

Motivated by 5] we describe a method related to scattered Hermite interpolation for which the solution of elliptic partial diierential equations by collocation is well-posed. We compare the method of 5] with our method. x1. Introduction In this paper we discuss the numerical solution of elliptic partial diierential equations using a collocation approach based on radial basis functions. To make ...

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...

This study modifies and discusses the application of a complete meshless method based on Shepard approximation with an emphasis on the detailed description of this computational technique and its numerical implementations. A new weighting function would be suggested. The global shape function and its derivatives are built based only on the discretisation of the domain in nodes. To deal with the...

The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial differential equations (PDEs), an emerging method for solving PDEs on surfaces, ...

We present a unified framework for interpolation and regularisation of scalarand tensor-valued images. This framework is based on elliptic partial differential equations (PDEs) and allows rotationally invariant models. Since it does not require a regular grid, it can also be used for tensor-valued scattered data interpolation and for tensor field inpainting. By choosing suitable differential op...

rainfall erosivity is the ability of rainfall to detach the soil particles. this study was conducted to evaluate spatial variability of rainfall erosivity indices in khouzestan province. the point data of indices (ei30, aim, ke>1 and onchev indices) in 74 stations were used to generate spatial erosivity maps through deterministic and geostatistical interpolation methods (radial basis functions,...

The local radial basis function (RBF) interpolation method enables very large-scale data sets to be handled efficiently, overcoming the drawbacks of global interpolation which produces highly ill-conditioned linear systems. Whereas there have been intensive studies on the accuracy of global RBF interpolation, the error analysis of local RBF interpolation is much less investigated. In this regar...