THE PARALLEL SUM OF MATRICES AND ITS APPLICATION IN GEODETIC ADJUSTMENTS

It is well known that for the comparison and combination of geodetic n etworks their heterogeneous datum definitions are well to be considere d. Various algorithms have been developed for this purpose. As an alte rnative concept to deal with hybrid datum problems, the operator paral lel sum of matrices is introduced in this paper. To begin with, a defi nition is given and some basic properties are explained. To demonstrat e the usefulness of the operator, two practical applications are given . The first deals with the estimation of parameters describing the def ormation of two networks which are to be compared to each other. The s econd one treats the estimation of parameters representing the heterog eneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that - regardless of the datum defin itions of the preadjusted individual networks - the parallel sum of ma trices can be used to simplify the algorithms applied for the estimati on of those parameters.