Solving algebraic computational problems
β Joseph L. Awange, Erik W. Grafarend
π Library
π
2005
π Springer
π English
β¦ LIBER β¦
π
Solving Algebraic Computational Problems in Geodesy and Geoinformatics: The Answer to Modern Challenges
β Scribed by Dr.-Ing. Joseph L. Awange, Prof. Dr.-Ing. habil. Erik W. Grafarend (auth.)
- Publisher
- Springer Berlin Heidelberg
- Year
- 2005
- Tongue
- English
- Leaves
- 344
- Category
- Library
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No coin nor oath required. For personal study only.
β¦ Synopsis
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.
β¦ Table of Contents
Introduction....Pages 1-6
Basics of Ring Theory....Pages 7-16
Basics of Polynomial Theory....Pages 17-28
Groebner Basis....Pages 29-45
Polynomial Resultants....Pages 47-55
Gauss-Jacobi Combinatorial Algorithm....Pages 57-76
Local versus Global Positioning Systems....Pages 77-88
Partial Procrustes and the Orientation Problem....Pages 89-104
Positioning by Ranging....Pages 105-146
From Geocentric Cartesian to Ellipsoidal Coordinates....Pages 147-164
Positioning by Resection Methods....Pages 165-198
Positioning by Intersection Methods....Pages 199-216
GPS Meteorology in Environmental Monitoring....Pages 217-244
Algebraic Diagnosis of Outliers....Pages 245-258
Transformation Problem: Procrustes Algorithm II....Pages 259-292
Computer Algebra Systems (CAS)....Pages 293-301
β¦ Subjects
Geophysics/Geodesy;Computer Applications in Geosciences;Geographical Information Systems/Cartography;Math. Applications in Geosciences;Geography (general)
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