The solution of linear inverse problems in satellite geodesy by means of spherical spline approximation

Abstract.

In this paper we consider a certain class of geodetic linear inverse problems in a reproducing kernel Hilbert space setting to obtain a bounded inverse operator . For a numerical realization we assume to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the Hilbert spaces. By applying to the obtained spline interpolant we get an approximation of the solution . Finally our main task is to show some properties of the approximated solution and to prove convergence results if the data set increases.