Bela Palancz – författare

This second edition of the book that targets those in computer algebra and artificial intelligence introduces Black Hole algorithm that is essential for optimizing hyperparameters, an important task in machine learning where mostly, stochastic global methods are used as well as ChatGPT, a novel and in the last few years, very popular Generative AI technology. In addition, fisher discriminant, a linear discriminant that can provide an optimal separation of objects, and the conversion of time series into images thereby making it possible to employ convolution neural network to classify time series effectively are presented.

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.

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