A heuristic and evolutionary algorithm to optimize the coefficients of curve parametrizations
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/44835DOI: 10.1016/j.cam.2016.03.020
ISSN: 0377-0427
Publisher
Elsevier
Date
2016-10-15Funders
Ministerio de Economía y Competitividad
The Austrian Research Promotion Agency
Bibliographic citation
Sendra, J. R. & Winkler, S.M., 2016, “A heuristic and evolutionary algorithm to optimize the coefficients of curve parametrizations”, Journal of Computational and Applied Math., vol. 305, pp. 18-35
Keywords
Rational curve
Parametrization height
Heuristic algorithm
Evolutionary algorithm
Arithmetic optimality
Description / Notes
A major part of this work was developed while S. M. Winkler was visiting J.R. Sendra at the Universidad de Alcalá in the frame of the project Giner de los Rios. J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683).
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
K-Projekt HOPL (The Austrian Research Promotion Agency (FFG))
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2016.03.020Rights
Attribution-NonCommercial-Noderivatives 4.0 International (CC BY-NC-ND 4.0)
© 2016 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
Parametric representations may have unnecessarily huge integer coefficients. This can be a computational problem in practical applications. In this paper we present an evolutionary algorithm that reduces the maximum length of the coefficients for a proper curve parametrization with integer coefficients. This method is tested with different families of parametrizations, and as we show the results are very satisfactory in terms of achievable quality and runtime consumption. According to our knowledge, this is the first algorithmic approach to this problem.
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