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Informations about the package levenberg-marquardt
Levenberg Marquardt Curve Fitting
This algorithm is based on the article Brown, Kenneth M., and J. E. Dennis. "Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation." Numerische Mathematik 18.4 (1971): 289-297. and http://people.duke.edu/~hpgavin/ce281/lm.pdf
In order to get a general idea of the problem you could also check the Wikipedia article.
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This package is a PHP port of mljs/levenberg-marquardt. As such, we have retained their MIT license.
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