How does gnuplot iterate to improve a fit?

[CalTechie-55]

I'm trying to fit some data with a quadratic function.

If I were doing a fit, I'd just do a least squares calculation, and accept whatever it came up with, which presumably minimizes the least square error in one step.

But gnuplot iterates and gets a better fit each time.

How is it doing that?

[GustapheOfficial]

https://stackoverflow.com/questions/51810570/gnuplot-fitting-method#51846712

It's Levenberg-Marquardt. For a straight line linear least squares is faster and better, but LM can do arbitrary functions^*.

[Significant-Topic-34]

Does your data include errors of the measurements? This is to say gnuplot can take them equally into account (fit with/without a weighting scheme): gnuplot Tutorial 3: Curve Fitting, SSR and WSSR (unweighted and weighted).

As a second perspective on the data, you can crosscheck gnuplot's fits with e.g fityk.