While preparing and teaching 'Introduction to Geodesy I and II' to
undergraduate students at Stuttgart University, we noticed a gap which
motivated the writing of the present book: Almost every topic that we
taught required some skills in algebra, and in particular, computer
algebra! 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
have attempted to put together basic concepts of abstract algebra which
underpin the techniques for solving algebraic problems. Algebraic
computational 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, the concepts and techniques presented herein are nonetheless
applicable 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
algebraic 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.
