Multistep interpolation of scattered data by compactly supported radial basis functions requires hierarchical subsets of the data. This paper analyzes thinning algorithms for generating evenly distributed subsets of scattered data in a given domain in IR. AMS subject classification: 41A15, 65D05, 65D07.

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produ...

Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...

AhtractThis paper discusses the rationale for employing alternative basis functions to the ubiquitous Gaussian in Radial Basis Function networks. In particular we concentrate upon employing unbounded basis functions (though the network as a whole remains bounded), and non positive definite basis functions. The use of unbounded and nonpositive basis functions, though counterintuitive in applicat...

Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...

A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral repr...

This paper analyses the application of Radial Basis Function (RBF) networks in grade interpolation. These networks are a very unique member of the family of Artificial Neural Networks. RBF networks have such theoretical properties that establish them as a potential alternative to existing grade interpolation techniques. Their suitability to the problem of grade interpolation will be demonstrate...

In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor elds are investigated and a decomposition formula is described. It is pointed out that the decomposition formula is of importance for the spectral analysis of the gra-vitational tensor in (spaceborne) gradiometry. Tensor spherical harmonics are introduced ...

This paper presents a new data-driven approach for modeling haptic responses of textured surfaces with homogeneous anisotropic grain. The approach assumes unconstrained tool-surface interaction with a rigid tool for collecting data during modeling. The directionality of the texture is incorporated in modeling by including 2 dimentional velocity vector of user’s movement as an input for the data...