Estimates for local approximations of functions on differential manifold
In this paper, approximations by splines, piecewise linear functions, and by other means, to functions on manifolds are analysed. The approach is two-fold: the approximations either take place via tangent planes, or the approximations are carried out by formulating the manifold in a nearby fashion by employing approximating relations. Convergence estimates and error estimates are provided. As a very important special case, the sphere as a manifold is considered, and as a particular choice of means to approximate, interpolation methods are used in another special case.
scientific article; zbMATH DE number 7394448