Bulletin géodésique

, Volume 65, Issue 1, pp 14–17 | Cite as

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

  • Piotr Laskowski


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Borkowski, K.M., (1989) Accurate algorithms to transform geocentric to geodetic coordinates, pp.50–56,Bulletin Geodesique 63 CrossRefGoogle Scholar
  2. Bowring, B.R., (1976) Transformation from spatial to Geographical Coordinates, pp.323–327,Survey Review, XXIII,181 Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Piotr Laskowski
    • 1
  1. 1.Intergraph CorporationHuntsvilleUSA

Personalised recommendations