Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?
- Piotr LaskowskiAffiliated withIntergraph Corporation
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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.
- Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?
Volume 65, Issue 1 , pp 14-17
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- Piotr Laskowski (1)
- Author Affiliations
- 1. Intergraph Corporation, 35894-0001, Huntsville, Alabama, USA