Summary
Two iterative algorithms for transformation from geocentric to geodetic coordinates are compared for numerical efficiency: the well known Bowring's algorithm of 1976, which employs the method of simple iteration, and the recent (1989) algorithm by Borkowski, which employs the Newton-Raphson method. The results of numerical tests suggest that the simple iteration method implemented in Bowring's algorithm executes approximately 30% faster than the Newton-Raphson method implemented in Borkowski's algorithm. Only two iterations of each algorithm are considered. Two iterations are sufficient to produce coordinates accurate to the comparable level of 1E-9 m, which exceeds the requirements of any practical application. Therefore, in the class of iterative methods, the classical Bowring's algorithm should be the method of choice.
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References
Borkowski, K.M., (1989) Accurate algorithms to transform geocentric to geodetic coordinates, pp.50–56,Bulletin Geodesique 63
Bowring, B.R., (1976) Transformation from spatial to Geographical Coordinates, pp.323–327,Survey Review, XXIII,181
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Laskowski, P. Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?. Bulletin Géodésique 65, 14–17 (1991). https://doi.org/10.1007/BF00806337
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DOI: https://doi.org/10.1007/BF00806337