Bulletin géodésique

, Volume 65, Issue 1, pp 14–17

Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?

  • Piotr Laskowski

DOI: 10.1007/BF00806337

Cite this article as:
Laskowski, P. Bulletin Géodésique (1991) 65: 14. doi:10.1007/BF00806337


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.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Piotr Laskowski
    • 1
  1. 1.Intergraph CorporationHuntsvilleUSA

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