# Default algorithm in NonlinearModelFit

Does anyone know the default algorithm used in NonlinearModelFit? The documentation gives several possible algorithms, but I can't figure out what it uses if you do not specify the algorithm.

Thanks.

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• The Answer to 21823 has some information. – bbgodfrey Feb 9 '15 at 0:08

With Method -> Automatic, the Wolfram Language uses the quasi-Newton method unless the problem is structurally a sum of squares, in which case the Levenberg-Marquardt variant of the Gauss-Newton method is used.

To confirm, I use the first example in FindFit >> Options >> Method and compare the output for various settings for the Method option:

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", and "QuasiNewton", with the default being Automatic.

model = a Exp[-b (x - c)^2] + d Sin[ω x + ϕ];
data = Table[{x, model /. {a -> 2, b -> 1, c -> 0, d -> 2, ω -> 0.67, ϕ -> 0.1}},
{x, -5, 5, .1}] + RandomReal[.25, 101];