Abstract. We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initialboundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the inter...

This paper presents a novel formulation for static limit analysis of structures, which the Airy stress function is approximated using stabilized Radial Point Interpolation Mesh-free method (RPIM). The field determined as second-order derivatives function, and equilibrium equations are automatically satisfied priori. so-called Stabilized Conforming Nodal Integration (SCNI) employed to ensure pre...

This article describes an approach based on hierarchical radial basis functions to reconstruction and modification of motion / image data, which are formulated as problems of scattered data interpolation. Assuming little about the data and choosing highly scalable / well adjustable basis functions, the approach can handle both the reconstruction and the manipulation in a unified and widely appl...

A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (h...

It is known that interpolation with radial basis functions of the same shape can guarantee a non-singular interpolation matrix, whereas little is known when one uses various shapes. In this paper, we prove that a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and ready local geometrical property of the interpolation points, we c...