# 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

## 1 Answer

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];

methods = {Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt",
"Newton", "NMinimize", "QuasiNewton"};

nlms = Quiet@ NonlinearModelFit[data, model, {a, b, c, d, ω, ϕ}, x,
Method -> #]["ParameterTable"] & /@ methods;
Grid[Partition[Labeled[#, #2, Top] & @@@ Transpose[{nlms, methods}], 3], Spacings -> {5, 5}]

• Perfect! Thank you so much. – user3037237 Feb 9 '15 at 14:33
• @user3037237, my pleasure. Welcome to mma.se. – kglr Feb 9 '15 at 15:34
• How to tell if Mathematica thinks your problem is a sum of squares? is there anyway to query the fit to ask what it used? – Tom Mozdzen Oct 12 '18 at 2:31
• @TomMozdzen, good question. I don't know the answer ottomh. – kglr Oct 12 '18 at 7:03
• @kglr I suppose I could use your code above and substitute my fitting equation and a sample data set and compare outputs as you have done above. Finding out should be a single simple command I would think. Do you know where the various methods are documented? I haven't found the page where they give you the full list of options. – Tom Mozdzen Oct 12 '18 at 7:23