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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.

Cosmic Physics --- Physics --- Physical Sciences & Mathematics --- Geospatial data --- Geodesy --- Mathematical geography. --- Mathematics. --- Geography, Mathematical --- Data, Geospatial --- Geographic information systems --- Geography --- Astronomical geography --- Geographical positions --- Physical geography. --- Computer science --- Civil engineering. --- Algebra --- Electronic data processing. --- Geophysics/Geodesy. --- Computational Mathematics and Numerical Analysis. --- Civil Engineering. --- Symbolic and Algebraic Manipulation. --- Numeric Computing. --- Data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Engineering --- Public works --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Automation --- Mathematics --- Geophysics. --- Computer mathematics. --- Computer science—Mathematics. --- Numerical analysis. --- Mathematical analysis --- Geological physics --- Terrestrial physics --- Earth sciences

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The book introduces the latest methods and algorithms developed in machine and deep learning (hybrid symbolic-numeric computations, robust statistical techniques for clustering and eliminating data as well as convolutional neural networks) dealing not only with images and the use of computers, but also their applications to visualization tasks generalized by up-to-date points of view. Associated algorithms are deposited on iCloud.

Machine learning. --- Learning, Machine --- Artificial intelligence --- Machine theory --- Remote sensing. --- Optical data processing. --- Geophysics. --- Space sciences. --- Remote Sensing/Photogrammetry. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Geophysics/Geodesy. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Science and space --- Space research --- Cosmology --- Science --- Astronomy --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Remote-sensing imagery --- Remote sensing systems --- Remote terrain sensing --- Sensing, Remote --- Terrain sensing, Remote --- Aerial photogrammetry --- Aerospace telemetry --- Detectors --- Space optics --- Optical equipment

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Space research --- Geophysics --- Electronics --- Telecommunication technology --- Computer. Automation --- optische communicatie --- optische elektronica --- datacommunicatie --- ruimtevaart --- geofysica --- sensoren

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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.

Mathematics --- Geodesy. Cartography --- Meteorology. Climatology --- Geology. Earth sciences --- General ecology and biosociology --- Environmental protection. Environmental technology --- Geography --- geodesie --- atmosfeerchemie --- atmosfeerfysica --- GIS (geografisch informatiesysteem) --- metrologie --- milieukunde --- cloud computing --- wiskunde --- geologie --- milieutechnologie --- atmosfeer

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This second edition of Mathematical Geosciences book adds five new topics: Solution equations with uncertainty, which proposes two novel methods for solving nonlinear geodetic equations as stochastic variables when the parameters of these equations have uncertainty characterized by probability distribution. The first method, an algebraic technique, partly employs symbolic computations and is applicable to polynomial systems having different uncertainty distributions of the parameters. The second method, a numerical technique, uses stochastic differential equation in Ito form; Nature Inspired Global Optimization where Meta-heuristic algorithms are based on natural phenomenon such as Particle Swarm Optimization. This approach simulates, e.g., schools of fish or flocks of birds, and is extended through discussion of geodetic applications. Black Hole Algorithm, which is based on the black hole phenomena is added and a new variant of the algorithm code is introduced and illustrated based on examples; The application of the Gröbner Basis to integer programming based on numeric symbolic computation is introduced and illustrated by solving some standard problems; An extension of the applications of integer programming solving phase ambiguity in Global Navigation Satellite Systems (GNSSs) is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. Three alternative algorithms are suggested, two of which are based on local and global linearization via McCormic Envelopes; and Machine learning techniques (MLT) that offer effective tools for stochastic process modelling. The Stochastic Modelling section is extended by the stochastic modelling via MLT and their effectiveness is compared with that of the modelling via stochastic differential equations (SDE). Mixing MLT with SDE also known as frequently Neural Differential Equations is also introduced and illustrated by an image classification via a regression problem.

Earth sciences. --- Environmental sciences—Mathematics. --- Geography—Mathematics. --- Mathematical physics. --- Physical geography. --- Geophysics. --- Earth Sciences. --- Mathematical Applications in Environmental Science. --- Mathematics of Planet Earth. --- Mathematical Methods in Physics. --- Earth System Sciences. --- Geography --- Physical mathematics --- Physics --- Mathematics --- Geological physics --- Terrestrial physics --- Earth sciences --- Geosciences --- Environmental sciences --- Physical sciences