       Re: Fitting Explicit Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg6845] [mg6845] Re: [mg6780] Fitting Explicit Functions
• From: jpk at max.mpae.gwdg.de
• Date: Thu, 24 Apr 1997 02:44:27 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> Hello,
>
> I would like to fit some data to an implicit function. I have data for x and y
> for the following equation:
>
> 1/x = exp( b*y/x ).
>
> I would like to fit for b. It appears that one cannot use the
> Levenberg-Marquardt method in Mathematica because that method takes the
> derivatives wrt the parameters explicitly. However, using the method of
> steepest descent (FindMinimum), the derivatives are taken numerically,
> so it should work. Nevertheless, I have not been able to do this.
>
> Below is an example. The data are such that the parameter b = -0.5. Does
anyone
> have any ideas of how to do this in Mathematica?
>
>
> Todd Culman
> Physics Dept.,
> The Ohio State University
>
Hi Todd,

try to fit instead of x against 1/x=xp, You can allways

model= y /.Flatten[Solve[xp==Exp[b*y*xp],y]]

and fit with

NonlinearRegress[
data /. {x_?NumberQ,y_}:>N[{1/x,y}],
model,{xp},{b,-.1,-2}]

and You get beside som error messages b->-0.733333333.

Hope that helps
Jens

```

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