Mishra, SK (2006): Least Squares Fitting of ChacónGielis Curves by the Particle Swarm Method of Optimization.

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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 ChacónGielis 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 curvefitting exercise may be satisfactory, a lack of uniqueness of ChacónGielis parameters to data (from which they are estimated) poses an insurmountable difficulty to interpretation of findings.
Item Type:  MPRA Paper 

Original Title:  Least Squares Fitting of ChacónGielis Curves by the Particle Swarm Method of Optimization 
Language:  English 
Keywords:  Least squares multimodal nonlinear curvefitting; Ricardo Chacón; Jacobian Elliptic functions; Weierstrass ; Gielis superformula; supershapes; Particle Swarm method; Repulsive Particle Swarm method of Global optimization; nonlinear programming; multiple suboptima; global; local optima; fit; empirical; estimation; cellular automata; fractals 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  466 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  15. Oct 2006 
Last Modified:  08. Jan 2014 11:27 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/466 