A KIND OF HERMITE INTERPOLATION ON THE SPHERE
关于球面上的一种Hermite插值

The purpose of this paper is to put forward a kind of Hermite interpolation schemes for the unit sphere surface. Firstly, we have studied Hermite interpolation on a set of coaxial circumferences along the sphere surface, and given three kinds of properly posed sets of interpolating functionals for it. Secondly, we have studied Hermite interpolation on the sphere surface, and proposed a superposition interpolation method, namely, the circumferences-superposition method. Combining these two results, we deduced a kind of properly posed set of interpolating functionals for Hermite interpolation on the sphere surface. In order to explain this method, we have given some concrete examples for structuring the properly posed set of interpolating functionals with lower degree and some numerical examples at the end of this paper.