ITERATIVE METHODS USED IN OVERLAP ASTROMETRIC REDUCTION TECHNIQUES DONOT ALWAYS CONVERGE

In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurrin g in overlapping reduction methods of astrometry do not always converg e. We exhibit examples of divergence. We then analyze an alternative a lgorithm proposed by Wang (1985). We prove the consistency of this alg orithm and verify that it can be convergent while the Gauss-Seidel met hod is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.