Abstract
In geodesy and geoinformatics, most problems are nonlinear in nature and often require the solution of systems of polynomial equations. Before 2002, solutions of such systems of polynomial equations, especially of higher degree remained a bottleneck, with iterative solutions being the preferred approach. With the entry of Groebner basis as algebraic solution to nonlinear systems of equations in geodesy and geoinformatics in the pioneering work “Gröbner bases, multipolynomial resultants and the Gauss Jacobi combinatorial algorithms : adjustment of nonlinear GPS/LPS observations”, the playing field changed. Most of the hitherto unsolved nonlinear problems, e.g., coordinate transformation, global navigation satellite systems (GNSS)’s pseudoranges, resection-intersection in photogrammetry, and most recently, plane fitting in point clouds in laser scanning have been solved. A comprehensive overview of such applications are captured in the first and second editions of our book Algebraic Geodesy and Geoinformatics published by Springer. In the coming third edition, an updated summary of the newest techniques and methods of combination of Groenbner basis with symbolic as well as numeric methods will be treated. To quench the appetite of the reader, this presentation considers an illustrative example of a two-dimension coordinate transformation problem solved through the combination of symbolic regression and Groebner basis.
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References
Awange, J.L.: Gröbner bases, multipolynomial resultants and the Gauss Jacobi combinatorial algorithms: adjustment of nonlinear GPS/LPS observations (2002)
Awange, J.L., Grafarend, E.W.: Solving Algebraic Computational Problems in Geodesy and Geoiormatics. Springer, Berlin (2005)
Awange, J.L., Grafarend, E.W., Paláncz, B., Zaletnyik, P.: Algebraic Geodesy and Geoinformatics. Springer, Berlin (2010)
Awange, J.L., Kiema, J.B.K.: Environmental Geodesy, monitoring and management. Springer, Berlin (2013)
Grafarend, E.W., Awange, J.L.: Applications of Linear and Nonlinear Models. Springer, Berlin (2012)
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Awange, J., Paláncz, B., Lewis, R. (2014). Groebner Basis in Geodesy and Geoinformatics. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_57
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DOI: https://doi.org/10.1007/978-3-662-44199-2_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
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