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The direct and inverse geodetic problems based on the M0L0DENSKII's closed for mulas were solved by the iteration computation method for non-linear function equation system. The results of numerical examples are as follows.(1) In medium and large distance problems having 40 km-120 km, the final converged values were obtained after two or three iterations with the accuracy of 1"×10-12 in angle and 1×10-8 cm in distance as shown in Table I.(2) In the case of short distance problem having the latitude and longitude differences of both 1" and elevation difference of 400 m between two geodetic points, however, an error of 5"×10-11 or so still remained after 8 iteration computations. Furthermore, in a very short distance problem (the latitude and longitude differences of both 0.1" and elevation difference of 400 m), about 10 iterations were required for obtaining the accuracy of 1"×10-10. The reason of such slow convergent speed in the iteration for solving short distance problems seems to originate from the socalled cancelling error, which appears in the computation of formulas containing the form of the subtraction of nearly equal two terms such as MOLODENSKII's formulas.
日本測地学会の論文