Solving Algebraic Computational Problems in Geodesy and Geoinformatics : The Answer to Modern Challenges / by Joseph L. Awange, Erik W. Grafarend.

Springer eBooks

Basics of Ring Theory -- Basics of Polynomial Theory -- Groebner Basis -- Polynomial Resultants -- Gauss-Jacobi Combinatorial Algorithm -- Local versus Global Positioning Systems -- Partial Procrustes and the Orientation Problem -- Positioning by Ranging -- From Geocentric Cartesian to Ellipsoidal Coordinates -- Positioning by Resection Methods -- Positioning by Intersection Methods -- GPS Meteorology in Environmental Monitoring -- Algebraic Diagnosis of Outliers -- Transformation Problem: Procrustes Algorithm II -- Computer Algebra Systems (CAS).

The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems using computer algebra techniques of Ring, polynomials, Groebner basis, resultants, Gauss-Jacobi combinatorial and Procrustes algorithms. Although these problems are traditionally solved by approximate methods, this book presents alternative algebraic techniques based on computer algebra tools. This new approach meets such modern challenges as resection by laser techniques, solution of orientation in robotics, transformation and bundle block adjustment in geoinformatics, densification of engineering networks, analytical solution for GPS-meteorology and many other problems. For mathematicians the book provides some practical examples of abstract algebra application and multidimensional scaling.

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