Abstract
We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations.
Keywords
- Intersection Point
- Singular Value Decomposition
- Polynomial System
- Multiple Root
- Quotient Ring
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Busé, L., Khalil, H., Mourrain, B. (2005). Resultant-Based Methods for Plane Curves Intersection Problems. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_7
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DOI: https://doi.org/10.1007/11555964_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28966-1
Online ISBN: 978-3-540-32070-8
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