A general radial quasi-interpolation operator on the sphere

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is a important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain Πm = Πm(IR ) the d–variate polynomials of degree ≤ m. In particular, the reproduction of Πm leads to an approximation order of m + 1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the ...

A Quasi-Local Interpolation Operator Preserving the Discrete Divergence

An overlapping additive Schwarz preconditioner for interpolation on the unit sphere by spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and earth science in which the sphere is taken as a model for the earth. When spherical basis functions are used to construct the interpolant, the underlying linear systems are ill-conditioned. In this paper, we present an additive Schwarz preconditioner to accelerate the solution process. An esti...

An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and earth science in which the sphere is taken as a model for the earth. Spherical radial basis functions provide a convenient tool to construct the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner to accel...

Vector Field Rbf Interpolation on a Sphere

This paper presents a new approach for Radial Basis Function (RBF) interpolation on a sphere. Standard approaches use the Euclidian metrics for the distance calculation of two points. However, for interpolation on a sphere, more naturally is computation of the distance as the shortest distance over the surface on a sphere, i.e. spherical distance of two points is more natural for interpolation ...