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fitting a curve by adjusting exponents

• Subject: [mg3254] fitting a curve by adjusting exponents
• From: wself at viking.emcmt.edu (Will Self)
• Date: 21 Feb 1996 09:35:05 -0600
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.
• Sender: daemon at wri.com

I'm sorry, I lost the original post.  Someone wanted to fit a function
of the form func[x,y,z,w] = a x^b + c y^d + e z^f + g w^h to some data
points.

Here's what I would suggest.  Write the usual expression ERR for the
sum of the squares of the errors.  Calculate the gradient of ERR
with respect to the 8 variables a through h.  Starting with your best
guess (from your physics) as to the actual values of the variables, 
do a gradient search to minimize the total error.  In doing the
gradient search, you might as well go ahead at each step and minimize
ERR + t*grad[ERR] as a function of t.

Will Self