Why does fitting terminate after 40 iteration ?

Look at DisplayHelpTopic "Special Variables for Curve Fitting". That explains how to change the maximum number of iterations

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Also, any fit that still has not converged at 40 iterations probably has an "identifiability" problem. Since you are still using Igor 6, here is a section I added to the Curve Fitting help in Igor 7 about identifiability problems:

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In addition to off-diagonal elements of the correlation matrix that are near 1 or -1, symptoms of identifiability problems include fits that require a large number of iterations to converge, or fits in which the estimated coefficient errors (W_sigma wave) are unreasonably large.

The phrase "identifiability problems" describes a situation in which two or more of the fit coefficients trade off in a way that makes it nearly impossible to solve for the values of both at once. They are correlated in a way that if you adjust one coefficient, you can find a value of the other that makes a fit that is nearly as good.

When the correlation is too strong, the fitting algorithm doesn't know where to go and therefore wanders around in a coefficient space in which a broad range of values all seem about as good. That is, broad regions in chi-square space provide very little variation in chi-square. The usual result is apparent convergence but with large estimated values in W_sigma, or a singular matrix error.

The error estimates are based on the curvature of the chi-square surface around the solution point. A flat-bottomed chi-square surface, such as results from having many solutions that are nearly as good, results in large errors. The flat bottom of the chi-square surface also results in small derivatives with respect to the coefficients that don't give a good indication of where the fit should go next, so iterations wander around, giving rise to fits that require many iterations to converge.

If you see a fit with unreasonably large error estimates, or that take many iterations to converge, compute the correlation matrix and look for off-diagonal values near 1 or -1. In our experience, values about 0.9 are probably OK. Values near 0.99 are suspicious but can be acceptable. Values around 0.999 are almost certainly an indication of problems.

Unfortunately, there is little you can do about identifiability problems. It is a mathematical characteristic of your fitting function. Sometimes a model has regions in coefficient space where two coefficients have similar effects on a fit, and expanding the range of the independent variable can alleviate the problem. Occasionally some feature controlled by a coefficient might be very narrow and you can fix the problem with higher sampling density.
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John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

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Thanks :)

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