Altaxo.Calc.Regression Namespace

It minimizes
sum(f - y)^2 + sum(lambda* f'(p))
where y are the data, f are the smoothed data, and f'(p) is the p-th
derivative of the smoothed function evaluated numerically. In other
words, the filter imposes a penalty on the p-th derivative of the
data, which is taken as a measure of non-smoothness.
Smoothing increases with increasing value of lambda.

The current implementation works up to p = 5; usually one should use
p = 2 or 3.

For points far from the boundaries of the data series, the frequency
response of the smoother is given by

   1/(1+lambda* (2-2* cos(omega))^2p);

where n is the order of the penalized derivative and
omega = 2 * pi * f / fs, with fs being the sampling frequency
(reciprocal of the distance between the data points).

Note that strong smoothing leads to numerical noise (which is smoothed
similarly to the input data, thus not obvious in the output).
For lambda = 1e9, the noise is about 1e-6 times the magnitude of the
data. Since higher p values require a higher value of lambda for
the same extent of smoothing (the same bandwidth), numerical noise
is increasingly bothersome for large p, but not for p <= 2.