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This book showcases powerful new hybrid methods that combine
numerical and symbolic algorithms. Hybrid algorithm research is
currently one of the most promising directions in the context of
geosciences mathematics and computer mathematics in general. One
important topic addressed here with a broad range of applications
is the solution of multivariate polynomial systems by means of
resultants and Groebner bases. But that's barely the beginning, as
the authors proceed to discuss genetic algorithms, integer
programming, symbolic regression, parallel computing, and many
other topics. The book is strictly goal-oriented, focusing on the
solution of fundamental problems in the geosciences, such as
positioning and point cloud problems. As such, at no point does it
discuss purely theoretical mathematics. "The book delivers hybrid
symbolic-numeric solutions, which are a large and growing area at
the boundary of mathematics and computer science." Dr. Daniel Li
chtbau
Improved geospatial instrumentation and technology such as in laser
scanning has now resulted in millions of data being collected,
e.g., point clouds. It is in realization that such huge amount of
data requires efficient and robust mathematical solutions that this
third edition of the book extends the second edition by introducing
three new chapters: Robust parameter estimation, Multiobjective
optimization and Symbolic regression. Furthermore, the linear
homotopy chapter is expanded to include nonlinear homotopy. These
disciplines are discussed first in the theoretical part of the book
before illustrating their geospatial applications in the
applications chapters where numerous numerical examples are
presented. The renewed electronic supplement contains these new
theoretical and practical topics, with the corresponding
Mathematica statements and functions supporting their computations
introduced and applied. This third edition is renamed in light of
these technological advancements.
Improved geospatial instrumentation and technology such as in laser
scanning has now resulted in millions of data being collected,
e.g., point clouds. It is in realization that such huge amount of
data requires efficient and robust mathematical solutions that this
third edition of the book extends the second edition by introducing
three new chapters: Robust parameter estimation, Multiobjective
optimization and Symbolic regression. Furthermore, the linear
homotopy chapter is expanded to include nonlinear homotopy. These
disciplines are discussed first in the theoretical part of the book
before illustrating their geospatial applications in the
applications chapters where numerous numerical examples are
presented. The renewed electronic supplement contains these new
theoretical and practical topics, with the corresponding
Mathematica statements and functions supporting their computations
introduced and applied. This third edition is renamed in light of
these technological advancements.
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.
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