[Data regression] Levenberg-Marquardt BUT force to intersect 2 KNWON points

[berlinkind]

Hi,

I have a large data set (2D Coordinates with errors) and i am using the Levenberg-Marquardt method to estimate the best polynomial function.
That part is working fine.

Now in my data set are exactly two KNOWN data points that are 100% correct. Therefore I want my function to go through these two points and fit the curve considering the other datapoints.

My polynom currently looks like
$$y=a_3*x^3+a_2*x^2+a_1*x+a_0$$

One idea I had, was to weight the two known points with very high values. But the result still is not correct.

Any Ideas – or maybe an idea of a totally other solution is welcome. I'm working more than a week on LM :-(

Thanks

 

[mXSCNT]

Well, if your function must go through (x1, y1) and (x2, y2) exactly, then you can use those values to calculate a2 and a3, given a1 and a0 (find the formula for them by hand). So instead of optimizing a function in 4 parameters you just optimize a function in 2 parameters, a1 and a0.