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dc.contributor.authorAwange, Joseph
dc.contributor.authorPalancz, B.
dc.contributor.authorLewis, R.
dc.contributor.editorHong, Hoon, Yap, Chee
dc.date.accessioned2017-01-30T15:18:09Z
dc.date.available2017-01-30T15:18:09Z
dc.date.created2014-06-17T20:00:16Z
dc.date.issued2014
dc.identifier.citationAwange, J. and Palancz, B. and Lewis, R. 2014. Groebner Basis in Geodesy and Geoinformatics, in Hong, H. and Yap, C. (ed), Mathematical Software ICMS - 2014, pp. 367-373. Berlin: Springer.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/45040
dc.description.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 problems, global navigation satellite systems (GNSS)'s pseudoranges, resection-intersection problems 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 Groebner 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.

dc.publisherSpringer
dc.subjectGeodesy
dc.subjectGNSS
dc.subjecttransformation problems
dc.subjectGroebner basis
dc.subjectGeoinformatics
dc.subjectnonlinear polynomial systems
dc.titleGroebner Basis in Geodesy and Geoinformatics
dc.typeBook Chapter
dcterms.source.startPage367
dcterms.source.endPage373
dcterms.source.titleMathematical Software ICMS - 2014
dcterms.source.isbn978-3-662-44198-5
dcterms.source.placeBerlin
dcterms.source.chapter108
curtin.departmentDepartment of Spatial Sciences
curtin.accessStatusFulltext not available


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