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MathGroup Archive 2011

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FindMinimum and Levenberg method

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119551] FindMinimum and Levenberg method
  • From: Grzegorz <gangrelek at poczta.fm>
  • Date: Thu, 9 Jun 2011 05:45:06 -0400 (EDT)

Hello,
I attempt to fit experimental data using FindMinimum function with Levenberg-Marquardt (LM) method (Mathematica 7). I know that the problem can be solved with FindFit function (or other methods of finding minimum), but I really have to use FindMinimum function and LM method. Therefore, I would appreciate if someone could explain how to use FindMinimum function to fit a set of experimental points (with LM method). 

Let's say that I have to fit a function f(x,a,b), where a and b are fit  parameters, to a dataset that looks like this:{{x1,y1},...,{xn,yn}}.
1. How to define "Residual"? Is this a vector V of a form {y1-f(x1,a,b),...,yn-f(xn,a,b)}? 
2. How to define the objective function? Is this 1/2(V.V) or V.V or something else?
I would be grateful for any help with this issue.
Regards,
G.


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