09.01.2012 21:30, josef.pktd@gmail.com kirjoitti: [clip]
One impression I had when I tried this out a few weeks ago, is that the spline smoothing factor s is imposed with equality not inequality. In the examples that I tried with varying s, the reported error sum of squares always matched s to a few decimals. (I don't know how because I didn't see the knots change in some examples.)
As far as I understand the FITPACK code, it starts with a low number of knots in the spline, and then inserts new knots until the criterion given with `s` is satisfied for the LSQ spline. Then it adjusts k-th derivative discontinuities until the sum of squares of errors is equal to `s`. Provided I understood this correctly (at least this is what was written in fppara.f): I'm not so sure that using k-th derivative discontinuity as the smoothness term in the optimization is what people actually expect from "smoothing". A more likely candidate would be the curvature. However, the default value for the splines is k=3, cubic, which yields a somewhat strange "smoothness" constraint. If this is indeed what FITPACK does, then it seems to me that the approach to smoothing is somewhat flawed. (However, it'd probably best to read the book before making judgments here.) Pauli