Spline Smooth

Uses cubic splines to smooth a grid. The important step in smoothing is the value of smoothing parameter. The smoothing parameter (p) determines the relative weight you would like to place on the contradictory demands of having f be smooth vs having f be close to the data. For p = 0, f is the least-squares straight line fit to the data, while, at the other extreme, i.e., for p = 1, f is the variational, or natural cubic spline interpolant. As p moves from 0 to 1, the smoothing spline changes from one extreme to the other. The interesting range for p is often near 1/(1+h^3/6), with h the average spacing of the data sites, and it is in this range that the default value for p is chosen. For uniformly spaced data, one would expect a close following of the data for p = 1/(1+h^3/60) and some satisfactory smoothing for p = 1/(1+h^3/0.6). You can input a p > 1, but this leads to a smoothing spline even rougher than the variational cubic spline interpolant.

Copyright <2010>, <Joaquim Luis>

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