Re: Smoothing vs. Fitting Splines
- To: mathgroup at smc.vnet.net
- Subject: [mg7208] Re: [mg7171] Smoothing vs. Fitting Splines
- From: Edgar Camacho Cota <ecc at ds5000.super.unam.mx>
- Date: Fri, 16 May 1997 02:30:45 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Tue, 13 May 1997, Peter Buttgereit wrote: > Dear Mathgroup, > in an earlier message I have asked about experiences with the > implementation of Smoothing Splines. > I think I had better defined what I meant with smoothing splines... > > Smoothing Splines - contrary to Fitting Splines (SplineFit.m) - do not > interpolate data points but represent an estimate of the smooth part of a > data series. > The basic idea is that the more often a function g is differenciable and > the smaller the value g^(k) of the low differenciation order k of that > function, the smoother it will look like. Usually you take k = 2. On the > other hand, you want g to have something to do with your data. > So you have to compromise between these two demands: > > Smoothness: minimise Intergrate [ d^2 g(t) / dt^2 ]^2 dt > > Data representation: minimise Sum [ (data(ti) - g(ti) )^2 ] > > the latter being the least squares approach. > > All in all, the task is then to minimise > > beta^2 Sum [ g(ti) - 2 g(ti-1) + g(ti-2)]^2 + Sum [data(ti) - g(ti)]^2 > > with beta^2 as a Lagrange parameter for smoothness. > > Does someone know of a good implementation (in Mathematica)? > I have scanned MathSource; Prest et al. "Numerical recipes..." don't help, > either... > > Thanks in advance, > Peter > > In mathSource exist some implementation of Savinsky Golay Low Pass Filter for Smoothing set of sampling data. this function like a filter for smoothing that show the book Numerical Recipes ...