Smooth Approximation of Data on the Sphere with Splines

摘要

A computable function, defined over the sphere, which is of class C sup 1 at least and which approximates a given set of data is constructed. The construction is based mainly upon tensor product spline basis functions, while at the poles of the spherical system of coordinates modified basis functions, suggested by spherical harmonics, are introduced to recover the continuity order at these points. Convergence experiments, refining the grid, are performed. The approximation accuracy is compared with that of the expansion in spherical harmonics. The use of piecewise approximation, with locally supported basis functions, versus approximation with spherical harmonics is discussed.