Homotopy Solution of Nonlinear Systems

Joseph L. Awange (), Béla Paláncz (), Robert H. Lewis () and Lajos Völgyesi ()
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Joseph L. Awange: Curtin University, Department of Spatial Sciences, School of Earth and Planetary Sciences
Béla Paláncz: Budapest University of Technology and Economics, Department of Geodesy and Surveying, Faculty of Civil Engineering
Robert H. Lewis: Fordham University
Lajos Völgyesi: Budapest University of Technology and Economics, Department of Geodesy and Surveying, Faculty of Civil Engineering

Chapter 2 in Mathematical Geosciences, 2023, pp 39-76 from Springer

Abstract: Abstract The concept and types of linear and nonlinear homotopy are introduced. Techniques for solving nonlinear equations and systems are discussed, such as regularization and automatic generation of start systems in case of algebraic systems. Their extension for non-polynomial systems and the possibility of parallel computation are discussed. Applications to geodesical problems, such as 3D resection and GPS positioning in case of N satellites, are presented.

Date: 2023
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DOI: 10.1007/978-3-030-92495-9_2

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