Interpolation on the sphere: a fast solution technique

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 ...

Polynomial interpolation on the unit sphere II

The problem of interpolation at (n+1) points on the unit sphere S by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

Matrix-free Interpolation on the Sphere

We study a subspace of bivariate trigonometric polynomials for interpolating functions on the sphere. We give an explicit construction for a system of interpolation nodes, and the corresponding basis for this space, that allows a (discrete) fast Fourier transform–type formula for the interpolant. We prove that the uniform norm of our interpolation operator is of the order (log M)2, where M is t...

Interpolation on the Unit Sphere Ii

The problem of interpolation at (n + 1) 2 points on the unit sphere S 2 by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

Polynomial Interpolation on the Unit Sphere