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