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Clustering Complex Zeros of Triangular System of Polynomials

Rémi Imbach 1 Marc Pouget 2 Chee Yap 1
2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This paper gives the first algorithm for finding a set of natural ε-clusters of complex zeros of a triangular system of polynomials within a given polybox in C^n, for any given ε > 0. Our algorithm is based on a recent near-optimal algorithm of Becker et al (2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is numeric, produces guaranteed results and is based on subdivision. We implemented it and compared it with state of the art solvers on various triangular systems, including systems with clusters of solutions or multiple solutions.
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Contributor : Marc Pouget <>
Submitted on : Monday, December 9, 2019 - 1:42:21 PM
Last modification on : Tuesday, March 3, 2020 - 4:00:11 PM
Long-term archiving on: : Tuesday, March 10, 2020 - 2:34:17 PM


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  • HAL Id : hal-01825708, version 3
  • ARXIV : 1806.10164



Rémi Imbach, Marc Pouget, Chee Yap. Clustering Complex Zeros of Triangular System of Polynomials. CASC 2019 - 21st International Workshop on Computer Algebra in Scientific Computing, Aug 2019, Moscow, Russia. ⟨hal-01825708v3⟩



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