"The focus of this book is clearly on applications of contemporary mathematical concepts and algorithms using HSNC. ... This book is also suitable for undergraduate-level classes with some background in linear algebra, in particular for courses emphasizing computation with high-level CAS software." (Eric L. Geist, Pure and Applied Geophysics, Vol. 177, 2020)
"This book deals with versatile aspects of numerical and symbolic computing solutions to systems of polynomial equations, optimization of systems, and data processing and modeling with applications in the domain of geoscience ... . The text is written in a clear and didactic way which makes the book a valuable literature for a broad spectrum of readers from graduate students, professionals in computer programing techniques, to those solving concrete practical problems in geoscience and other fields." (Vladimir Cadez, zbMATH 1394.86001, 2018)

Solution of algebraic polynomial systems.- Homotopy solution of nonlinear systems.- Over and underdeterminated systems.- Simulated annealing.- Genetic algorithm.- Particle swarm optimization.- Integer programming.- Multiobjective optimization.- Approximation with radial bases functions.- Support vector machines (SVM).- Symbolic regression.- Quantile regression.- Robust regression.- Stochastic modeling.- Parallel computations.

Professor Joseph Awange joined the Department of Spatial Sciences (Curtin University, Australia) in 2006 under a Curtin Research Fellowship and concurrently undertook the prestigious Alexander von Humboldt (AvH) Fellowship at the Geodetic Institute (Karlsruhe Institute of Technology, Germany) having been awarded the Australian 2008-2011 Ludwig Leichhardt Memorial Fellowship for experienced researchers. In 2015, he won all the three major Fellowship Awards: Alexander von Humboldt (Germany), Japan Society of Promotion of Science (Japan) and Brazil Frontier of Science (Brazil) to carry out research in those countries. At Curtin University, he is currently engaged in teaching and research having attracted more than $1.5M worth of research grants. He obtained his BSc and MSc degrees in Surveying from the University of Nairobi (Kenya), and was also awarded a merit scholarship by the German Academic Exchange Program (DAAD), which facilitated his obtaining a second MSc degree and PhD in Geodesy at Stuttgart University (Germany). In 2002-2004, he was awarded the prestigious Japan Society for Promotion of Science (JSPS) Fellowship to pursue postdoctoral research at Kyoto University (Japan). Prof Awange attained International Editorial role in Springer Earth Science Books and has authored 11 scholarly books with the prestigious Springer publishers and more than 130 peer-reviewed high impact journal publications (in e,g., Remote Sensing of Environment, Journal of Climate, Climatic Change, Advances in Water Resources, International Journal of Climatology, and Journal of Hydrology among others).

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

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