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Homotopy Solution of Nonlinear Systems

In: Mathematical Geosciences

Author

Listed:
  • 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)

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.

Suggested Citation

  • Joseph L. Awange & Béla Paláncz & Robert H. Lewis & Lajos Völgyesi, 2023. "Homotopy Solution of Nonlinear Systems," Springer Books, in: Mathematical Geosciences, edition 2, chapter 2, pages 39-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-92495-9_2
    DOI: 10.1007/978-3-030-92495-9_2
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