I tested this inversion against 3 known analytical abel pairs and found good agreement with this numerical solution. I found that with smooth data with good signal/noise, increasing upf provided a better answer.

I was able to get the code working by replacing lsqcurvefit with a standard non-linear equations solver and simply supplying the residuals. Everything seems to be ok but I still need to through a few theoretical test curves at it. Thanks!

22 Oct 2013

LMFnlsq2
Solution of one or more nonlinear equations in the least squares sense.
Author: Miroslav Balda

Would it be possible to use this code without having the optimization toolbox (lsqcurvefit function)? Does it simply find a scaled coefficient for each of the vectors?