Implementation of a Near-Optimal Complex Root Clustering Algorithm

Rémi Imbach, Victor Y. Pan, Chee Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationMathematical Software – ICMS 2018 - 6th International Conference, Proceedings
PublisherSpringer-Verlag
Pages235-244
Number of pages10
ISBN (Print)9783319964171
DOIs
StatePublished - Jan 1 2018
Event6th International Conference on Mathematical Software, ICMS 2018 - South Bend, United States
Duration: Jul 24 2018Jul 27 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10931 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Mathematical Software, ICMS 2018
CountryUnited States
CitySouth Bend
Period7/24/187/27/18

Fingerprint

Clustering algorithms
Clustering Algorithm
Roots
Natural Computing
Maple
Optimal Algorithm
Argand diagram
Polynomials
Benchmark
Polynomial
Integer
Software

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Imbach, R., Pan, V. Y., & Yap, C. (2018). Implementation of a Near-Optimal Complex Root Clustering Algorithm. In 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.

Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings. Springer-Verlag, 2018. p. 235-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10931 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Imbach, R, Pan, VY & Yap, C 2018, Implementation of a Near-Optimal Complex Root Clustering Algorithm. in 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
Imbach R, Pan VY, Yap C. Implementation of a Near-Optimal Complex Root Clustering Algorithm. In Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings. Springer-Verlag. 2018. p. 235-244. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-96418-8_28
Imbach, Rémi ; Pan, Victor Y. ; Yap, Chee. / Implementation of a Near-Optimal Complex Root Clustering Algorithm. Mathematical Software – ICMS 2018 - 6th International Conference, Proceedings. Springer-Verlag, 2018. pp. 235-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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