| A method for fast evaluation of band-limited functions by means of bi-variate interpolation at many scattered points on the unit 2-d sphere is presented. The method relies on the stability and efficiency of the Barycentric Lagrange interpolation as it is applied in two directional orientations on a mesh grid of points. It is fast, numerically stable, and utilizes an error bound formula to achieve a sharp prescribed error bound based on the grid size and choice of points included in interpolation. In this paper, we discuss how this method can be applied for approximation on the sphere of band-limited functions (spherical polynomials), and in the realm of geodesy to accurately evaluate the geoid undulation and other geodetic quantities on the sphere. To achieve this we develop an algorithm and its software realization in Matlab. Comparison of this algorithm with another existing algorithm referenced in the literature is also presented. |
