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Re: Fittings 2 sets of equations and 2 data sets with nonlinearmodelfit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121709] Re: Fittings 2 sets of equations and 2 data sets with nonlinearmodelfit
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Mon, 26 Sep 2011 20:06:02 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On 09/26/2011 03:14 AM, JamesE wrote:
> Hi,
>
> My names is James Ellison; and I have 2 nonlinear equations of the type:
>
> y[1]=x+a*x[1]^2+b*x[1]^3 and y[2]=a*x[2]^3+b*x[2]^5 with the real valued parameters a and b for both equations.
>
> I further have 2 data sets
>
> data[1] for y[1] and
> data[2] for y[2]
>
> I can use NonlinearModelFit in order to fit each data[i] set to its function y[i] and get good fits. But the parameters a and b should be the same.
>
> How can I create a simple code with Mathematica, so that I can do a simultaneous fit resulting in the parameters a and b to be the same.
>
> I am a Mathematica beginner and would be pleased, if someone could answer my question for beginners.
>
> Best regards, James

Ways of going about this are described in notes at the URLs below. The 
rough idea is to contsruct one model that switches between two forms 
based discrete values of a new dimension parameter. Could be, say, 1 for 
the first data set and 2 for the second one.

http://forums.wolfram.com/mathgroup/archive/2004/Oct/msg00031.html

http://forums.wolfram.com/mathgroup/archive/2006/Apr/msg00011.html

http://forums.wolfram.com/mathgroup/archive/2006/Apr/msg00020.html

http://forums.wolfram.com/mathgroup/archive/2010/Apr/msg00280.html

Daniel Lichtblau
Wolfram Research




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