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Applications of Numerically Solving Polynomial Systems

In: Nankai Symposium on Mathematical Dialogues

Author

Listed:
  • Jonathan D. Hauenstein

    (University of Notre Dame, Department of Applied and Computational Mathematics and Statistics)

Abstract

The problem of solving systems of polynomial equations is ubiquitous throughout science and engineering. The mathematical subject of numerical algebraic geometry consists of a collection of approaches for numerically solving polynomial systems with one foundational technique being homotopy continuation. This short manuscript summarizes using homotopy continuation on two different problems. In the first problem, homotopy continuation is used to approximate a critical parameter value where two solutions of a parameterized differential equation merge together. In the second problem, homotopy continuation is used to compute critical points of a sum of squares best fit function for given data.

Suggested Citation

  • Jonathan D. Hauenstein, 2026. "Applications of Numerically Solving Polynomial Systems," Springer Books, in: Yang-Hui He & Mo-Lin Ge & Cheng-Ming Bai & Jiakang Bao & Edward Hirst (ed.), Nankai Symposium on Mathematical Dialogues, pages 173-179, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-2328-9_20
    DOI: 10.1007/978-981-19-2328-9_20
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