### Abstract

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 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.

Original language | English (US) |
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Title of host publication | Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings |

Publisher | Springer-Verlag |

Pages | 235-244 |

Number of pages | 10 |

ISBN (Print) | 9783319964171 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 6th International Conference on Mathematical Software, ICMS 2018 - South Bend, United States Duration: Jul 24 2018 → Jul 27 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10931 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Conference on Mathematical Software, ICMS 2018 |
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Country | United States |

City | South Bend |

Period | 7/24/18 → 7/27/18 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings*(pp. 235-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10931 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-96418-8_28

**Implementation of a Near-Optimal Complex Root Clustering Algorithm.** / Imbach, Rémi; Pan, Victor Y.; Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10931 LNCS, Springer-Verlag, pp. 235-244, 6th International Conference on Mathematical Software, ICMS 2018, South Bend, United States, 7/24/18. https://doi.org/10.1007/978-3-319-96418-8_28

}

TY - GEN

T1 - Implementation of a Near-Optimal Complex Root Clustering Algorithm

AU - Imbach, Rémi

AU - Pan, Victor Y.

AU - Yap, Chee

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85050619158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050619158&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-96418-8_28

DO - 10.1007/978-3-319-96418-8_28

M3 - Conference contribution

AN - SCOPUS:85050619158

SN - 9783319964171

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 235

EP - 244

BT - Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings

PB - Springer-Verlag

ER -