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Rapport (Rapport De Recherche) Année : 2018

Implementation of a Near-Optimal Complex Root Clustering Algorithm

Résumé

We describe Ccluster, a software for computing natural ε-clusters of complex roots in a given box of the complex plane. This algorithm from Becker et al. (2016) is near-optimal when applied to the benchmark problem of isolating all complex roots of an integer polynomial. It is one (Irina Voiculescu informed us that her student Dan-Andrei Gheorghe has independently implemented the same algorithm in a Masters Thesis Project (May 18, 2017) at Oxford University. Sewon Park and Martin Ziegler at KAIST, Korea, have implemented a modified version of Becker et al.~(2016) for polynomials having only real roots being the eigenvalues of symmetric square matrices with real coefficients) of the first implementations of a near-optimal algorithm for complex roots. We describe some low level techniques for speeding up the algorithm. Its performance is compared with the well-known MPSolve library and Maple.
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Dates et versions

hal-01822137 , version 1 (23-06-2018)

Identifiants

  • HAL Id : hal-01822137 , version 1

Citer

Rémi Imbach, Victor Y. Pan, Chee Yap. Implementation of a Near-Optimal Complex Root Clustering Algorithm. [Research Report] TU Kaiserslautern; City University of New York; Courant Institute of Mathematical Sciences, New York University. 2018. ⟨hal-01822137⟩

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