1998A&A...335..769R

The central overlap problem in astrometry has been revisited in the recent last years by Eichhorn (1988ApJ...334..465E) who explicitly inverted the matrix of a constrained least squares problem. In this paper, the general explicit solution of the unconstrained central overlap problem is given. We also give the explicit solution for an other set of constraints; this result is a confirmation of a conjecture expressed by Eichhorn (1988ApJ...334..465E). We also consider the use of iterative methods to solve the central overlap problem. A surprising result is obtained when the classical Gauss Seidel method is used; the iterations converge immediately to the general solution of the equations; we explain this property writing the central overlap problem in a new set of variables.