Algorithms for intersecting parametric and algebraic curves II: multiple intersections
Graphical Models and Image Processing
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Solving projective complete intersection faster
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
A New Criterion for Normal Form Algorithms
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Extracting Cylinders in Full 3D Data Using a Random Sampling Method and the Gaussian Image
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Solving Polynomial Equations: Foundations, Algorithms, and Applications (Algorithms and Computation in Mathematics)
Computing the topology of a real algebraic plane curve whose equation is not directly available
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
A numerical elimination method for polynomial computations
Theoretical Computer Science
The implicit equation of a canal surface
Journal of Symbolic Computation
Curve/surface intersection problem by means of matrix representations
Proceedings of the 2009 conference on Symbolic numeric computation
Computer Aided Geometric Design
An algorithm for addressing the real interval eigenvalue problem
Journal of Computational and Applied Mathematics
Rational univariate representations of bivariate systems and applications
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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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.