Subject: CCL:Fitting a potential by a family of functions...

From: Keith Refson <[email-masked]>
Date: Mon, 28 Sep 1998 15:59:08 +0100 (BST)

boufer writes:
 
 > I want to fit a potential~(of the Coulomb type) by some family of
 > functions. My problem is, I cannot use the classical least square method
 > in which we start by writing : 
 > 
 > D = Int (True Potential - approximation)^2 dv
 > 
 > since in this case the true potential is not square integrable and hence
 > yield to a divergence. 

Just remove the divergence using a weighting function, eg

D = Int ((True Potential - approximation)/r)^2 dv

will remove the r -> 0 divergence.  You will need to devise something
more complicated to include this as well as the r -> oo divergence

Keith Refson

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From: [email-masked]
Date: Mon, 28 Sep 98 12:45:57 EDT

Fitting a potential by a family of functions........

If there is a problem wiht the function not be square-integrqable, you will 
have to discretize the true potential and perform your least squares fit
using summatiions rather than integrations.
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