Browsing by Subject "Cartesian coordinates"

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Access status: Open Access ,
A comparison of iterative methods of the cubic rate convergence in the problem of transformation between Cartesian and geodetic coordinates
(2014) Bajorek, Maciej; Kulczycki, Marek; Ligas, Marcin
The problem of transformation between Cartesian and geodetic (ellipsoidal) coordinates occurs often in day-to-day geodetic practice. Thus, from years it attracts interest of many scientists and practitioners. Despite the fact that many algorithms of the conversion exist to this day one may still observe new methods and approaches to the problem. In this work a comparison as to the efficiency of iterative methods of the cubic rate convergence to the solution of 'latitude equation' in three representations has been presented. Two of them are polynomial representations (quartic equations) and one is in the form of an irrational equation. A comparison has been performed on two ellipsoidal height intervals: from -10 km to 10 km, from 10 km to 36 000 km and from 0° to 90° for the latitude.