[Solved] None linear interpolation.

[MvGulik]

whatever Edited February 7, 2011 by MvGulik

[jchd]

Is that still timing data with/without Sleep? (Just curious)

You don't have much data points here. Just having frequency for 4,5 and more importantly 9 would greatly help. If you post data, I'll fire another Mathematica session to have a nicer function fit (but I don't promise anything simple and reasonably accurate with that few data points).

Here's why I ask: the basic fitting uses polynomials to some degree. Without more constraints, you "see" that the curve is tempted to satisfy zeroes (n degree polynomial has up to n zeroes). Using other methods (non polynomial, like trigonometric or more complex) would make it worse in your case.

[MvGulik]

whatever Edited February 7, 2011 by MvGulik

[jchd]

Kriging on that few samples has no meaning. The method relies on assumptions that clearly lack here. It's very well suited to ground profiling for instance and is used intensively in this domain (on small scales). Larger scales use other methods.

The main problem with all the least squares methods is that they all claim to be the best, yet they can lead to completely different results depending on which method you select and which "parameter" you feed. And that's only the begining as you may as well bring on this Bezier, splines, B-splines, Beta-splines and their cohort of associated orthogonal polynomials (Bernstein, Tchebicheef, Legendre, Bessel, ...) and have even more "parameters" to choose. Every possible combination giving you, of course, "the best" result, proof in hand!

From this point of view, Lagrange is the simplest, makes no untold assumptions beside continuity and derivability and doesn't require you pick any "parameter" at random. Another method with even more benefits is what their author calls (well, could be called by now) "polar interpolation" by Paul de Faget de Casteljau.

But you know, I'm afraid all this discussion I'm shifting it outside AutoIt perimeter! You could nonetheless try to code a polar form (in the sense of De Casteljau) in AutoIt. I own all the books of Paul somewhere, but none handy. Maybe Google reminds him: yes, you find many links.

[MvGulik]

whatever Edited February 7, 2011 by MvGulik

[MvGulik]

whatever Edited February 7, 2011 by MvGulik

[jchd]

I'll get to answer you about this, but I just finds one major web source of information has been removed from public access few hours ago and I need to find a workaround asap. Sorry.