# Solving Algebraic Computational Problems in Geodesy and Geoinformatics

## The Answer to Modern Challenges

Authors: Awange, Joseph L., Grafarend, Erik W.

eBook $119.00 price for USA in USD (gross) • ISBN 978-3-540-26862-8 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase About this book While preparing and teaching ‘Introduction to Geodesy I and II’ to - dergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taughtrequiredsomeskillsinalgebra,andinparticular,computeral- bra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we haveattemptedtoputtogetherbasicconceptsofabstractalgebra which underpin the techniques for solving algebraic problems. Algebraic c- putational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds,theconceptsand techniquespresented hereinarenonetheless- plicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robotics apply resection and intersection techniques which require - gebraic solutions. Solution of nonlinear systems of equations is an indispensable task in almost all geosciences such as geodesy, geoinformatics, geophysics (just to mention but a few) as well as robotics. These equations which require exact solutions underpin the operations of ranging, resection, intersection and other techniques that are normally used. Examples of problems that require exact solutions include; • three-dimensional resection problem for determining positions and orientation of sensors, e. g. , camera, theodolites, robots, scanners etc. , VIII Preface • coordinate transformation to match shapes and sizes of points in di?erent systems, • mapping from topography to reference ellipsoid and, • analytical determination of refraction angles in GPS meteorology. ## Table of contents (16 chapters) • Introduction Pages 1-6 • Basics of Ring Theory Pages 7-16 • Basics of Polynomial Theory Pages 17-28 • Groebner Basis Pages 29-45$29.95
• Polynomial Resultants

Pages 47-55

eBook \$119.00
price for USA in USD (gross)
• ISBN 978-3-540-26862-8
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices

## Bibliographic Information

Bibliographic Information
Book Title
Solving Algebraic Computational Problems in Geodesy and Geoinformatics
Book Subtitle
Authors
2005
Publisher
Springer-Verlag Berlin Heidelberg