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I would like to fit a function to some experimental data such that the extracted value of Curie temperature (Tc) describes the temperature at which the response flattens out to a constant value. However, the expression I am trying to fit does not exist for values above Tc so I'm not able to converge the fit. From literature, I expect this material to have Tc = 353 C. The equation is

P=A/(T-Tc)^B + C

where P is the dependent variable, T is the independent variable, and the rest are fitting parameters. How can I bypass any errors that come up during the fitting process in order to converge the fit? Specifically the error I get is from

FindFit[data, P[t, A, B, Tc, C], {{A, 3000}, {B, 1}, {Tc, 353}, {C, 20}}, t]

and it says, "FindFit::nrjnum: The Jacobian is not a matrix of real numbers at {A,B,Tc,C} = {3000.,1.,353.,20.}." I am aware of what this means and I've seen previous posts about it but I'm just asking for general function manipulation advice that is suitable for Mathematica's FindFit.

Here are data points and my guess for the fit. The results from FindFit don't converge.

dataplot

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  • $\begingroup$ As there is not a lot of data, would be nice to have the data array so that we can experiment. $\endgroup$ – Picaud Vincent Jun 12 at 16:31
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    $\begingroup$ Of course: {{22, 5 Sqrt[377]}, {75, Sqrt[9687]}, {125, Sqrt[8243]}, {175, Sqrt[ 5767]}, {240, 2 Sqrt[906]}, {275, 28 Sqrt[2]}, {300, Sqrt[ 570]}, {325, Sqrt[345]}, {350, Sqrt[239]}, {375, Sqrt[118]}, {395, Sqrt[107]}} $\endgroup$ – user66091 Jun 12 at 16:38
  • $\begingroup$ Data of size 11 is too small for a reliable fit. $\endgroup$ – user64494 Jun 12 at 18:23
  • $\begingroup$ Can you please also give the estimated measurement error of each data point? $\endgroup$ – Roman Jun 12 at 18:43
  • $\begingroup$ I had left out the errorbars for simplicity. But here they are. Averaging over 3 measurements gives these values for the data points: {{22, 100.641}, {75, 98.3124}, {125, 92.6697}, {175, 77.3606}, {240, 59.8693}, {275, 38.5962}, {300, 23.}, {325, 18.3212}, {350, 14.9108}, {375, 10.9392}, {395, 10.3763}} and their associated errors are {32.6261, 6.86022, 19.4442, 13.532, 5.30309, 9.47399, 6.86469, 2.65322, 4.92755, 1.75818, 1.81654} $\endgroup$ – user66091 Jun 12 at 20:00

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