Fitting with a complex equation

• To: mathgroup at smc.vnet.net
• Subject: [mg18403] Fitting with a complex equation
• From: "Gibum Kim" <gibumk at tamu.edu>
• Date: Wed, 7 Jul 1999 00:11:03 -0400
• Organization: Texas A&M University, College Station, Texas
• Sender: owner-wri-mathgroup at wolfram.com

```Hi, there.
I'm having a trouble with the determining parameters of the equation with
the experimental data.
This is my equation.

f(x)=Abs[A/(wa-x-I Ga)+k E^(I t)]^2

A,wa,Ga,k and t are parameters I want to find.
I know the best guess of the parameters.
Even with the best guess values,  I got totally wrong values of them using
"FindMinimum".
Here's the program I got from mathematica support.

ClearAll[A,wa,Ga,k,t]
f=Abs[A/(wa + x - I Ga) +  k E^(I t)]^2
<<Statistics`
model[A_?NumberQ,wa_?NumberQ,Ga_?NumberQ,
k_?NumberQ,t_?NumberQ,x_?NumberQ]:=
Abs[A/(wa + x - I Ga) +  k E^(I t)]^2
sse[A_,wa_,Ga_,k_,t_]=
Plus @@ Apply[(model[A,wa,Ga,k,t,#1]-#2)^2 &, data,{1}];
FindMinimum[sse[A,wa,Ga,k,t],
{A,8.1,8.5},{wa,2958,2962},{Ga,8.2,8.6},
{k,0.3,0.4},{t,32,35},MaxIterations->500]

Do you have any idea?
Your any suggestion would be grateful.

```

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