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
EditorsJames H. Davenport, George Labahn, Josef Urban, Manuel Kauers
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

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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 J. H. Davenport, G. Labahn, J. Urban, & M. Kauers (Eds.), 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