IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/466.html
   My bibliography  Save this paper

Least Squares Fitting of Chacón-Gielis Curves by the Particle Swarm Method of Optimization

Author

Abstract

Ricardo Chacón generalized Johan Gielis's superformula by introducing elliptic functions in place of trigonometric functions. In this paper an attempt has been made to fit the Chacón-Gielis curves (modified by various functions) to simulated data by the least squares principle. Estimation has been done by the Particle Swarm (PS) methods of global optimization. The Repulsive Particle Swarm optimization algorithm has been used. It has been found that although the curve-fitting exercise may be satisfactory, a lack of uniqueness of Chacón-Gielis parameters to data (from which they are estimated) poses an insurmountable difficulty to interpretation of findings.

Suggested Citation

  • Mishra, SK, 2006. "Least Squares Fitting of Chacón-Gielis Curves by the Particle Swarm Method of Optimization," MPRA Paper 466, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:466
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/466/1/MPRA_paper_466.pdf
    File Function: original version
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mishra, SK, 2006. "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions," MPRA Paper 1743, University Library of Munich, Germany.

    More about this item

    Keywords

    Least squares multimodal nonlinear curve-fitting; Ricardo Chacón; Jacobian Elliptic functions; Weierstrass ; Gielis super-formula; supershapes; Particle Swarm method; Repulsive Particle Swarm method of Global optimization; nonlinear programming; multiple sub-optima; global; local optima; fit; empirical; estimation; cellular automata; fractals;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:466. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.