Fastest way to fit a parabola to set of points?

Question

Hi,

Given a set of points, what's the fastest way to fit a parabola to them? Is it doing the least squares calculation or is there an iterative way?

Thanks

Edit: I think gradient descent is the way to go. The least squares calculation would have been a little bit more taxing (having to do qr decomposition or something to keep things stable).

Answer 1

A calculated solution is almost always faster than an iterative solution. The "exception" would be for low iteration counts and complex calculations.

I would use the least squares method. I've only every coded it for linear regression fits but it can be used for parabolas (I had reason to look it up recently - sources included an old edition of "Numerical Recipes" Press et al; and "Engineering Mathematics" Kreyzig).

Answer 2

If the points have no error associated, you may interpolate by three points. Otherwise least squares or any equivalent formulation is the way to go.