Exact fitting of data is about not possible, consider this fact as a conjecture. An exact non-linear fit to data means retrieving the same coefficients that generated the data + some Gaussian noise [on the dependent calculated values]. Some functions will be recovered exactly , those cases are rare and not worth be repertoried.
Real data sets, data sets collected from DAC [Data Acquisition] are subject to several uncontrollable sources of inexactitude, called "noise" in popular terminology.
Major sources of inexactitudes:
1. Different time constants, hysteresis ... between the independent and the dependent domains X, Y
2. Ripple and precision from the digitization.
3. Precision of the measuring X, Y chains ... including global installation.
4. Poor or under designed measuring chains.
5. Quality of the setup, lab, personnel ...
6. Insufficient significant figures
7. ...
On the top of these elementary inexactitudes, then the statistical probabilities. When all combined and with not enough data and not enough data in some regions of the shape, data collection are far from exact, even far from near exact in most experiments. On the top again, perfect or non defective mathematical methods do not exist and can't exist [another conjecture].
All that to warn visitors that in this collab we can only return "best fit" as done. Often, after reconsidering a first attempt, a 2nd best fit is found or found by regular collaborators. It is also the responsibility of the visitors to provide or suggest the model when available from their in-house knowledge.
jmG
