Re: Curve fitting help needed


"Nicros" <da@xxxxxx> wrote in message
news:K8imf.37274$D13.12041@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi,
>
> I have a series of data points that I am fitting to a reference set. I
> am currently using a chebyshev polynomial approximation to minimize the
> error in the fit.
>
> However, outliers and erronious data points have been causing a huge
> headache.
>
> If there is one poor fitting data point, then all the good points that
> would fit perfectly (if this poor data point was removed) are fitted
> poorly. Removing the data points before fitting is not desireable,
> since I have no way of really knowing ahead of time which data points
> might be bad.
>
> Is there a minimization fitting routine or algorithm out there that will
> minimize the maximum number of datapoints to the highest degree
> possible, while allowing poor fit of outliers? So that if I have 10
> data points (for example) and one of them is significantly off, the
> algorithm allows this one point to shift as far as necessary to fit the
> other 9 perfectly? How about 5 and 5? No clue what would even need to
> happen here.
>
> I am not a mathmatician, Im a software engineer and I didnt find
> anything in numerical recipes in c++ that sounded like it could do this.
>
> Does such an algorithm even exist? Any suggestions or links are
> appreciated!
>
> Thanks,
> N


Maybe someone will point you to an algorithm, but if not you could try this.

Most fitting routines allow you to assign weights to each data point
according to how good you think the point is.
So fit once with all the weights = 1
Calculate the error (deviation) of each point from fitted curve.
Use new weights = 1/(1+|error|) for each point.
Refit
Maybe iterate a few times.

If your data is all over the place this may not converge, but it should do
if most points lie on the curve.





.

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