A General Computer Program for the Application of the Rigorous Blockadjustment Solution in Photographic Astrometry

The evaluation of stellar positions from overlapping plates by rigorous blockadjustment methods leads to a very large system of normal equations containing both, stellar positions and plate constants as unknowns. These general normal equations can be reduced to a subsystem with banded-bordered coefficient matrix, containing only the plate constants as unknowns. In the case of a large photographic net covering a hemisphere or sphere with multiple overlap of the plates, the actual number of unknown plate constants may exceed 20 000, depending on the adopted reduction model. The general structure of a computer program, now under development at the Hamburg observatory, is described in detail. The program, entirely written in FORTRAN IV language, is based on a very fast subroutine, developed at the University of Stuttgart, for the solution and inversion of large symmetric and positive-definite linear systems of equations with banded-bordered coefficient matrix. It provides a direct non-iterative solution of the blockadjustment problem with, at least, partial inversion of the normal equation matrix for evaluation of the standard deviations of the computed star positions at selected blockpoints. The choice of suitable reduction models and the application of the program for theoretical accuracy studies using inversion and simulation methods are discussed. Estimates of computing effort and external storage capacity as a function of the number of unknowns and the actual matrix-structure are obtained. For a variety of overlap patterns and blockstructures, occurring more frequently in photographic zone-work, simple analytic expressions for estimates of computing effort are quoted. In addition, ordering schemes for an optimal arrangement of the single plates according to minimum bandwidth of the reduced normal equation matrix are provided. Based on these results and adopting a CDC 7600 computer system, computing times and necessary external storage capacities are obtained for several large photographic nets. It is shown that a blockadjustment of the full sphere with multiple overlap can be provided within 3 hr computing time for the solution of the reduced normal equations containing 48 000 unknown plate constants.