convolution vs. NMinimize

• To: mathgroup at smc.vnet.net
• Subject: [mg52397] convolution vs. NMinimize
• From: db at ict.fhg.de (julia)
• Date: Thu, 25 Nov 2004 05:51:03 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I've had some problems with the nonlinear fit of my measuresd data
before.
Now, i have worked it out. I have to use a numerical global
optimization.
The fit with NMinimize leads to very good results.
The problem now is, that the fit needs about 6 hours computation time.
I'm sure this could be faster, but i don't have an idea how...

i've generated a sum of squares from the measured data and the model.
The model consists of the actual model and a numerical convolution of
the
model with a measured input signal. The convolution should be the the
time-consuming
step. I don't know what mathematica is doing exactly (e.g., which
steps are calculated
symbolical or numerical). The optimization should be fast, if the
model with the actual
parameters, and the convolution would be evaluated numerically.
I've attached the code for the optimization.

In[11]:=
pred[Pe_,tau_]:=Module[{model,pred1,falt},
model=(Pe*tau/(4*&#960;*t^3))^0.5*Exp[-Pe/(4*t/tau)*(1-t/tau)^2];
pred1=Map[model/.{t->#}&,time];falt=ListConvolve[inp,pred1,1];falt
]

In[15]:=soln=NMinimize[Plus@@Table[((yc[Pe,tau][[i]])-respconvdata[[i,2]])^2,
{i,Length[time]}],{{tau,15,20},{Pe,95,110}},MaxIterations->50,Method->"DifferentialEvolution"]//Timing

"inp" is the input signal
"pred" is the predicted Convolution product
"respconvdata" is the measured curve

Does anybody have an idea?
(e.g., how to apply the convolution on a different way..)

Thanks,

julia

```

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