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Nonlinear Systems of Equations in Geodesy

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
Piroska Zaletnyik
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Erik Grafarend
Organization: Stuttgart University
Department: Geodesy and Geoinformatics
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Dixon's resultant, a powerful mathematical tool is here proposed as an alternative to Groebner basis, Sylvester Resultant, Sturmfels Resultant or Multipolynomial Resultant for solving nonlinear system of equations in geodesy. We demonstrate its power in solving intersection, GPS ranging and C7 Conformal transformation problems. Its overraiding advantage compared to the other closed form solutions listed above is its small size which enables faster solution in-case of relatively small systems with 3-4 variables. Geodetic users uncomfortable with lengthy expressions of Groebner basis or Multipolynomial Resultant may find it useful.

(Editor's Note: It may be necessary to download this Mathematica package to properly execute the code in this notebook.)

*Applied Mathematics > Computer Science

Dixon Resultant, Nonlinear equations, Intersection, CAS
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DixonRealArticle_PB2_C7.nb (192.4 KB) - Mathematica Notebook [for Mathematica 5.2]